Error-detecting abilities of binary nonlinear constant weight codes

摘要

CONSTANT weight codes are very important in coding theory for its application to communication. In refs., the undetected error probabilities (UEP) of binary nonlinear constant weight codes (BNCW) were studied, and Wang et al, showed that when n > 8, BNCW codes (n, 2, TO) were not proper. Wang proposed a conjecture that when n >4δ and δ> 1, BNCW codes (n, 2δ, ω) are not proper. In this note, the error-detecting abilities of BNCW codes (n, 2δ, ω) are studied with another method. A necessary condition of BNCW codes being proper is presented, which implies that for considerably large n, BNCW codes (n, 2δ, ω) are not proper. The cases of 8 = 2, 3 are discussed in detail, which imply that there exist proper BNCW codes with length n >4δ. We thinkthat the conjecture in ref. should be modified as follows: when n >8δ, BNCW codes ( n, 2δ, ω) are not proper.