Abstract: A device and method of collision-free hashing of near-match inputs that includes the following components. An adder for receiving an input i, a check value cv, and outputs n, which is greater than or equal to the sum of i and cv. A checker for receiving a value n, a value d, a first polynomial, and an output at which the first polynomial appears if the checker determines that the first polynomial is of degree proportional to d and divides xn+1. A factorization block for factoring the first polynomial into a second polynomial and a third polynomial. A first division block for dividing an input of bit length i by the second polynomial to generate a first portion of the hash of the input. A second division block for dividing the input by the third polynomial to generate a second portion of the hash of the input.

Abstract: A method of collision-free hashing of near-match by selecting bit positions d that differ between a first input and a second input, selecting a degree of a first polynomial for a cyclic code proportional to d, selecting a bit length i of the first input and the second input, selecting a bit length cv of a check value greater than or equal to d, setting n>=i+cv, generating the first polynomial that divides xn+1, factoring the first polynomial into a second and a third polynomials, receiving the first input, dividing the first input by the second polynomial, dividing the first input by the third polynomial, and identifying the results of the last two steps as a hash of the first input.

Abstract: A method of encoding a communication signal by selecting a cyclic code, establishing a generator polynomial, generating a polynomial using the generator polynomial, forming a matrix from the generated polynomial, receiving data to be encoded, appending zeros to the received data, calculating a syndrome of the matrix, calculating check values from the syndrome, appending the check values to the received data, and encoding the received data with appended check values using the generator polynomial.

Abstract: A method of correcting a communication signal with BCH product codes is disclosed. The method comprising the steps of receiving a codeword vector, establishing a generator polynomial, establishing a check polynomial, calculating a binary-matrix, and calculating the binary syndrome S=Hrt. If an all zero vector results, no errors exist in the received vector. If errors exist, a tm x (N?k) binary matrix is created, the power basis expansion of (r(?1), r(?3), r(?5), . . . r(?2t?1)) is calculated, and the syndrome is solved. The speed of the method comes from using word-level XOR's to apply the check polynomial to the stream at all offsets. The utility of this approach is due in part to the fact that the conversion matrix involved can be created quickly using only items needed elsewhere in BCH decoders: a field table and the generator polynomial coefficients.