Author_Institution :
Dept. of Inf. Eng., Xidian Univ., Xi´´an, China
Abstract :
The undetected error probability (UEP) of binary (n, 2δ, m) nonlinear constant weight codes over the binary symmetric channel (BSC) is investigated, where n is the blocklength, m is the weight of codeword and 2δ is the minimum distance of the codes. The distance distribution of the (n, 2, m) nonlinear constant weight codes is evaluated. It is proven in this paper that the (5, 2, 2) code, (5, 2, 3) code, (6, 2, 3) code, (7, 2, 4) code, (7, 2, 3) code and (8, 2, 4) code are the only proper error-detecting codes in the (n, 2, m) nonlinear constant weight codes for n⩾5, in the sense that their UEP is increased monotonically with the channel error rate p, of course all these proper codes are m-out-of-n codes. Furthermore, it is conjectured that except for the cases of n⩽4δ, there are no proper error-detecting binary (n, 2δ, m) nonlinear constant weight codes, for n>8 and δ⩾1
Keywords :
binary sequences; coding errors; error detection codes; error statistics; probability; binary symmetric channel; blocklength; channel error rate; codeword weight; distance distribution; error-detecting codes; minimum code distance; nonlinear binary constant weight codes; undetected error probability; Automatic repeat request; Communications Society; Computer errors; Computer simulation; Error analysis; Error probability; Hamming distance; Helium; Linear code; Sufficient conditions;
