Bit-flip coding uses a bit-flip encoder to flip bits in a redundancy-intersecting vector of a binary array having n rows and n columns until Hamming weights of the binary array are within a predetermined range of n divided by two. Information bits of an input data word to the bit-flip coding apparatus are stored in locations within the binary array that are not occupied by n redundancy bits of a redundancy vector.

The disclosure relates to a method for identification via channels in a system having a plurality of data processing devices. The method comprises selecting, in a first data processing device, an identifier indicative of a target second data processing device of a plurality of second data processing devices; determining, in the first data processing device, an outer codeword from the identifier using an outer code comprising a first outer code and a second outer code; determining, in the first data processing device, an optical orthogonal codeword from the outer codeword using an optical orthogonal code; determining, in the first data processing device; a randomly selected codeword from the optical orthogonal codeword using an error correction code; and emitting the selected codeword from the first data processing device via a channel. Further, a computer program product and a system for identification via channels are provided.

Encoding or decoding can operate a processing system to apply one or more recursive relations to a known parameter associated with a length m and a Hamming weight l to produce a computed parameter associated with length m1. An encoding process can thus assign values to bits of a code based on comparison of the data value being encoded and the computed parameter. A decoding process can use the computed parameters in a calculation of a decoded data value.

Encoding or decoding can operate a processing system to apply one or more recursive relations to a known parameter associated with a length m and a Hamming weight l to produce a computed parameter associated with length m1. An encoding process can thus assign values to bits of a code based on comparison of the data value being encoded and the computed parameter. A decoding process can use the computed parameters in a calculation of a decoded data value.

A solution is proposed for error processing, wherein n byte error positions of n byte errors are predefined (where n is a positive integer), wherein this involves determining whether there is a further byte error position on the basis of the n byte error positions and on the basis of n+1 error syndrome components of a first error code.

Solutions are proposed related to error detection wherein (i) each byte of a second byte sequence is determined as a function of at least one byte of a first byte sequence, (ii) a byte of the second byte sequence is impermissible if it is not equal to an assigned byte of the first byte sequence and if no error of a predefined error set corrupts this byte to the assigned byte of the first byte sequence, and (iii) at least one error is detected if the second byte sequence is impermissible, the second byte sequence being impermissible if at least one byte of the second byte sequence is impermissible.

Solutions are proposed related to error detection wherein (i) each byte of a second byte sequence is determined as a function of at least one byte of a first byte sequence, (ii) the second byte series is permissible if (a) it equals the corresponding byte of the first byte sequence or (b) an error being a member of a predetermined error set could cause the byte of the second byte sequence to become the byte of the first byte sequence, and otherwise (c) the byte of the second byte sequence is impermissible, and (iii) at least one error is detected if the second byte sequence is impermissible.