Abstract: Methods and apparatus create codewords of n-state symbols having one of 3 or more states with n-state check symbols. Check symbols are created from independent expressions. Codewords are associated with a matrix for detection of one or more symbols in error and the location of such symbols in error. Symbols in error are reconstructed from symbols not in error, error syndromes and check symbols not in error. Deliberately created errors that can be corrected are used as nuisance errors.

Abstract: A sequence generator implemented on a receiver is synchronized with a sequence generator at a transmitter. The receiver receives k n-state symbols, with k>1 and n>1 wherein each of the k n-state symbols is associated with a generating state of the sequence generator at the transmitter. A processor in the receiver evaluates an n-state expression that generates an n-state symbol that is associated with a synchronized state of the receiver. Coefficients related to the n-state expression are stored on a memory and are retrieved by the processor. The synchronized state in one embodiment is part of a code hop. The sequence generator in the receiver may be part of a descrambler, of a communication device, of a data storage device and/or of an opening mechanism.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: Methods and apparatus for coding and decoding n-state symbols with n?2 and n>2 and n>3 and n>4 are provided wherein at least one implementation of an addition over an alternate finite field GF(n) and an inverter defined by a multiplication over the alternate finite field GF(n) are provided. Encoders and decoders implementing a single n-state truth table that is a truth table of an addition over an alternate finite field GF(n) modified in accordance with at least one inverter defined by a multiplication over the alternate finite field GF(n) are also provided. Encoders include scramblers, Linear Feedback Shift Register (LFSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders.

Abstract: An encoder creates an (p,k,n) n-state codeword with p n-state symbols of which k n-state symbols are data symbols, an n-state symbol being represented by a signal with n>2, p>2 and k>(p-k). Intermediate states of an encoder in forward and in reverse direction are provided in a comparative n-state expression and implemented on a processor. A plurality of signals representing a codeword with at least one n-state symbol in error is processed by the processor by evaluating the comparative n-state expression. A partial result of an expression is determined after a symbol has been received. An error location and an error magnitude are determined. The error is corrected by the processor.

Abstract: Maximum length properties of n-state sequences of n-state symbols with n=2 or n>2 are tested. Checkwords are generated from p consecutive n-state symbols in a sequence of n-state symbols which may overlap by (p?1) n-state symbols. If a sequence has np?1 n-state symbols in which 2 consecutive checkwords overlap in (p?1) n-state symbols and each checkword formed in the extended sequence is unique, then the sequence is a maximum length n-state sequence. An n-state feedback shift register based sequence generator with p n-state register elements is tested on the content of the shift register for np?1 cycles. If the shift register content is not repeated the sequence is maximum length. Generation of a sequence is stopped when the content repeats.

Abstract: Reversible and self reversing multi-value scrambling functions created by applying multi-value inverters are disclosed. The generation of possible multi-value inverters is also presented. Corresponding multi-value descrambling functions are also disclosed. The multi-value functions are used in circuits that scramble and descramble multi-value signals. The multi-value functions can also be used in signal generators. Such signal generators do not require the use of multipliers. The auto-correlation of the signals generated by the signal generators is also presented. Electronic circuits that implement the multi-value functions are also described.

Abstract: Methods and apparatus for coding and decoding n-state symbols with n?2 and n>2 and n>3 and n>4 are provided wherein at least one implementation of an addition over an alternate finite field GF(n) and an inverter defined by a multiplication over the alternate finite field GF(n) are provided. Encoders and decoders implementing a single n-state truth table that is a truth table of an addition over an alternate finite field GF(n) modified in accordance with at least one inverter defined by a multiplication over the alternate finite field GF(n) are also provided. Encoders include scramblers, Linear Feedback Shift Register (LFSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders.

Abstract: N-state with n equal or greater than 2 modified Linear Feedback Shift Registers (mLFSRs) having a non-reversible n-state switching function have been disclosed. An mLFSR can also contain a device that implements an n-state logic function of which one input is provided with a signal external to the mLFSR. The mLFSR can be in Fibonacci or in Galois configurations. N-state scramblers and corresponding descramblers applying an mLFSR are provided. N-state coding boxes apply non-reversible switching functions connected to n-state scrambling or descrambling functions. Sequence generators and detectors are also disclosed.

Abstract: Methods and apparatus to create and display screen stereoscopic and panoramic images are disclosed. Methods and apparatus are provided to generate multiple images that are combined into a stereoscopic or a panoramic image. A controller provides correct camera settings for different conditions. A controller rotationally aligns images of lens/sensor units that are rotationally misaligned. A compact controllable platform holds and rotates a camera. A remote computing device with a camera and a digital compass tracks an object causing the camera in the platform to track the object.

Abstract: An encoder creates an (p,k,n) n-state codeword with p n-state symbols of which k n-state symbols are data symbols, an n-state symbol being represented by a signal with n>2, p>2 and k>(p?k). Intermediate states of an encoder in forward and in reverse direction are provided in a comparative n-state expression and implemented on a processor. A plurality of signals representing a codeword with at least one n-state symbol in error is processed by the processor by evaluating the comparative n-state expression. A partial result of an expression is determined after a symbol has been received. An error location and an error magnitude or error value are determined. The error is corrected by the processor.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: Method and apparatus for generating ternary and multi-valued Gold sequences, are disclosed. Also methods to detect ternary and multi-valued sequences are disclosed. The detection can be performed by a ternary or multi-valued LFSR descrambler when the sequences are generated by an LFSR based sequence generator. A wireless system which can assign additional sequences to designated users is also disclosed. The wireless system can also transfer information to user equipment that enables methods for sequence generation and sequence detection.

Abstract: Multi-valued or n-state with n=2p Linear Feedback Shift Registers (LFSRs) in binary form are provided for scramblers, descramblers and sequence generators using addition and multiplication functions over a Finite Field GF(n) in binary form. N-state switching functions in an LFSR are implemented by using implementations of reversible binary functions. LFSRs may be in Fibonacci or in Galois configuration. N-state LFSR based sequence generators in binary form for generating an n-state maximum length sequence in binary form are also provided. A method for simple correlation calculation is provided. Communication systems and data storage systems using the LFSRs are also disclosed.

Abstract: Methods and apparatus to create and display panoramic images on a mobile device are disclosed. Such a mobile device can be a mobile phone. Apparatus is provided to control the position of a lens in relation to a reference lens. Methods and apparatus are provided to generate multiple images that are combined into a panoramic image. A panoramic image may be a static image. It may also be a video image. A controller provides correct camera settings for different conditions. An image processor creates a panoramic image from the correct settings provided by the controller. A panoramic camera is applied in a computer gaming system.

Abstract: Linear Feedback Shift Registers (LFSRs) based 2p state with p>2 or p?2 scramblers, descramblers, sequence generators and sequence detectors in binary implementation are provided. An LFSR may apply devices implementing a binary XOR or EQUIVALENT function, a binary shift register and binary inverters and binary state generator, wherein at least an output of one shift register element in a first LFSR is connected to a device implementing a reversible binary logic function is a second LFSR. They may also apply 2p state inverters using binary combinational logic are applied. Memory based binary 2p state inverters are also applied. Non-LFSR based n-state scramblers and descramblers in binary logic are also provided. A method for simple correlation calculation is provided. Communication systems and data storage systems applying the provided LFSR devices are also disclosed.

Abstract: An encoder creates an (p,k,n) n-state codeword with p n-state symbols of which k n-state symbols are data symbols, an n-state symbol being represented by a signal with n>2, p>2 and k>(p?k). Intermediate states of an encoder in forward and in reverse direction are provided in a comparative n-state expression and implemented on a processor. A plurality of signals representing a codeword with at least one n-state symbol in error is processed by the processor by evaluating the comparative n-state expression. A partial result of an expression is determined after a symbol has been received. An error location and an error magnitude or error value are determined. The error is corrected by the processor.

Abstract: Method and apparatus for writing scrambled multi-value data to a physical media and for reading scrambled multi-value data from a physical media, are disclosed. The physical media can be an optical disk. The scrambling can be performed by a multi-valued LFSR scrambler and the descrambling can be performed by a multi-valued LFSR descrambler. Further, the multi-valued data that is scrambled can include synchronization data and/or user data. Error correction coding can be used during the writing process and processing to correct for errors can be used during the reading process. Also, methods and apparatus for synchronizing multi-valued data written to and read from physical media are disclosed. Multi-value correlation methods and apparatus are also disclosed.

Abstract: Methods and apparatus for coding and decoding n-state symbols with n?2 and n>2 and n>3 and n>4 are provided wherein at least one implementation of an addition over an alternate finite field GF(n) and an inverter defined by a multiplication over the alternate finite field GF(n) are provided. Encoders and decoders implementing a single n-state truth table that is a truth table of an addition over an alternate finite field GF(n) modified in accordance with at least one inverter defined by a multiplication over the alternate finite field GF(n) are also provided. Encoders include scramblers, Linear Feedback Shift Register (LFSR) based encoders, sequence generator based encoders, block coders, streaming cipher encoders, transposition encoders, hopping rule encoders, Feistel network based encoders, check symbol based encoders, Hamming coder, error correcting encoders, encipherment encoders, Elliptic Curve Coding encoders and all corresponding decoders.