On generator matrices of MDS codes
IEEE Transactions on Information Theory
On the complete weight enumerator of Reed-Solomon codes
SIAM Journal on Discrete Mathematics
Constructions for Permutation Codes in Powerline Communications
Designs, Codes and Cryptography
The Grey-Rankin bound for nonbinary codes
Problems of Information Transmission
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Codes for MIMO transmission based on orthogonal sequences
Problems of Information Transmission
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We consider sequences in which every symbol of an alphabet occurs at most once. We construct families of such sequences as nonlinear subcodes of a q-ary [n, k, n 驴 k + 1] q Reed-Solomon code of length n 驴 q consisting of words that have no identical symbols. We introduce the notion of a bunch of words of a linear code. For dimensions k 驴 3 we obtain constructive lower estimates (tight bounds in a number of cases) on the maximum cardinality of a subcode for various n and q, and construct subsets of words meeting these estimates and bounds. We define codes with words that have no identical symbols, observe their relation to permutation codes, and state an optimization problem for them.