Abstract: Disclosed herein is a method of generating a coded data packet in dependence on a plurality of source data packets, the method comprising: determining a plurality of data packets, for generating a coded data packet, from a plurality of source data packets for encoding, wherein each of the plurality of source data packets for encoding comprises the same number of bits; generating a multiplied data packet in dependence on one or more multiplication operations between a multiplication value and bits of one of the determined data packets; and generating a coded data packet in dependence on a combination of the multiplied data packet and one or more of the other of said plurality of determined data packets that have not been multiplied; wherein the one or more multiplication operations are performed as operations in the finite field GF(p); p is greater than 2; the multiplication value is an element of the finite field GF(p); the multiplication value is not 0 or 1; and the combination of data packets is performed b

Abstract: Disclosed herein is a method for determining how to encode data in accordance with a systematic coding technique and encoding data in accordance with the determined systematic coding technique. The method includes: determining code parameters; determining source data nodes that comprise source data that is not encoded by the systematic coding technique; for each of the redundant nodes, determining to generate each of the substripes of data in dependence on a combination of a different substripe from each of the source data nodes; and determining each of one or more of the substripes of at least one of the redundant nodes to be further dependent on at least one further substripe of source data that it is not currently dependent on.

Abstract: Disclosed herein is a method of generating an encoded data packet over GF(2). The method comprises determining 303 a plurality of data packets in dependence on a Latin rectangle, wherein the plurality of data packets have equal length; and generating 305 an encoded data packet by bitwise XORing the determined plurality of data packets. The efficiency of encoding, decoding, and transmission over a network of data packets are all improved, as well as the security properties of the transmitted information.

Abstract: Disclosed herein is a method of generating a coded data packet in dependence on a plurality of source data packets, the method comprising: determining a plurality of data packets, for generating a coded data packet, from a plurality of source data packets for encoding, wherein each of the plurality of source data packets for encoding comprises the same number of bits; generating a multiplied data packet in dependence on one or more multiplication operations between a multiplication value and bits of one of the determined data packets; and generating a coded data packet in dependence on a combination of the multiplied data packet and one or more of the other of said plurality of determined data packets that have not been multiplied; wherein the one or more multiplication operations are performed as operations in the finite field GF(p); p is greater than 2; the multiplication value is an element of the finite field GF(p); the multiplication value is not 0 or 1; and the combination of data packets is performed b

Abstract: Disclosed herein is a method of generating an encoded data packet over GF(2). The method comprises determining 303 a plurality of data packets in dependence on a Latin rectangle, wherein the plurality of data packets have equal length; and generating 305 an encoded data packet by bitwise XORing the determined plurality of data packets. The efficiency of encoding, decoding, and transmission over a network of data packets are all improved, as well as the security properties of the transmitted information.

Abstract: Disclosed herein is a method of generating a generator matrix for defining how to systematically code source data, the method comprising: determining source nodes for comprising a plurality of sub-stripes of source data, wherein the number of source nodes is K and the number of sub-stripes of source data comprised by each source node is S; determining redundant nodes for comprising a plurality of sub-stripes of coded data, wherein the number of redundant nodes is R and the number of sub-stripes of coded data comprised by each redundant node is S; determining values of a first generator matrix according to a systematic coding technique such that K of the rows of the generator matrix to define how to generate all of the K source nodes as comprising source data and R of the rows of the first generator matrix define how to generate all of the R redundant nodes as comprising combinations of two or more of the source nodes; generating a second generator matrix, with a first dimension (K×S) and a second dimension ((

Abstract: Stream ciphers, including synchronous stream ciphers, self-synchronizing stream ciphers, and totally asynchronous stream ciphers, employ a working key and a quasigroup transformation, where the quasigroup used is based on an initial secret key. Error-correction and pseudo-random number generation improver methods also employ quasigroup transformations.

Abstract: Stream ciphers, including synchronous stream ciphers, self-synchronizing stream ciphers, and totally asynchronous stream ciphers, employ a working key and a quasigroup transformation, where the quasigroup used is based on an initial secret key. Error-correction and pseudo-random number generation improver methods also employ quasigroup transformations.