Abstract
CONSTAUT weight codes are very important in coding theory for its application to communication. In refs. [ 1-51, the undetected error probabilities ( U E P ) of binary nonlinear constant weight codes (BNCW) were studied, and Wang et a l . showed that when n > 8, BNCW codes ( n , 2, w ) were not proper. ~ a n g ' ~ ] proposed a conjecture that when n >46 and 6 > 1, BNCW codes ( n , 2 6 , w ) are not proper. In this note, the error-detecting abilities of BNCW codes ( n , 2 6 , w ) 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 , 2 6 , w ) are not proper. The cases of 6 = 2, 3 are discussed in detail, which imply that there exist proper BNCW codes with length n > 4 6 . We think that the conjecture in ref. [ 2 ] should be modified as follows: when n > 86, BNCW codes ( n , 2 6 , w ) are not proper.
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