Abstract: A device and method of determining candidates to decode by receiving a message, selecting m, identifying m voltages in message near zero volts, generating binary version of message, generating candidates that are variations of the binary message by varying the m positions, multiplying a modified binary message by the parity check matrix of the message, generating a matrix of the rows of the parity check matrix corresponding to the m positions, determining a rank v of the matrix, eliminating rows that are not linearly independent, determining if the sixth step result is in a span of the ninth step result, if so then there are 2m-1-2m-v(m?1) candidates, where the candidates can multiply the seventh step result to get the sixth step result and candidates with odd weights more than one Hamming distance from the candidates, otherwise there are 2m-1 candidates having odd weight.

Abstract: The present invention is a method of determining codeword boundary without marker bits by receiving transmission bits; determining a dual code of a code used to generate the transmission bits; selecting a vector from the dual code; initializing n scoring variables; initializing i=1; initializing z=1; selecting n bits from the transmission bits starting at bit position i; performing a bit-wise AND operation on the vector and the n selected bits; if the result of the bit-wise AND operation contains an even number of ones then assigning a value of zero to the result, otherwise assigning a value of one to the result; setting Sz equal to Sz plus the result of the last step; if z is less than n, incrementing z and i each by 1 and returning to the seventh step, otherwise proceeding to the next step; if z=n, i<L, and it is desired to process additional transmission bits then incrementing i by 1, and returning to the sixth step, otherwise proceeding to the next step; identifying the scoring var