Extended Binomial Moments of a Linear Code and the Undetected Error Probability
Problems of Information Transmission
Discrete Applied Mathematics
On the optimum distance profiles about linear block codes
IEEE Transactions on Information Theory
Hi-index | 754.90 |
Let C be an [n,k,d]q linear code. The defect of C is the parameter s=s(C)=n-k+1-d. If k⩾m+1⩾2 then by the Griesmer bound d⩽(qm(q-1)/qm-1)(s+m). The author's interest is in those linear codes having the maximum minimum distance, i.e., d=(qm(q-1)/qm-1)(s+m). For m=1 we have d=q(s+1) and the codes are maximum minimum distance (MMD) codes in the sense of Faldum and Willems (see ibid., vol.44, p.1555-58, 1998). Thus we consider MMD codes in a more general sense. We refer to them simply as MMD codes. All MMD codes with m=1 are known up to formal equivalence. Note that two codes are formally equivalent if they have the same weight distribution. The author classifies up to formal equivalence the MMD codes with m⩾2