An improved upper bound on covering radius
Proceedings of the 2nd international conference, AAECC-2 on Applied algebra, algorithmics and error-correcting codes
Some optimal codes from algebraic geometry and their covering radii
European Journal of Combinatorics
Some Upper Bounds on the Covering Radii of Linear CodesOver \F_q and Their Applications
Designs, Codes and Cryptography
On the generalized Hamming weights of cyclic codes
IEEE Transactions on Information Theory
Generalized Hamming weights of q-ary Reed-Muller codes
IEEE Transactions on Information Theory
On the inherent intractability of certain coding problems (Corresp.)
IEEE Transactions on Information Theory
List decoding from erasures: bounds and code constructions
IEEE Transactions on Information Theory
Bounds on the minimum support weights
IEEE Transactions on Information Theory
AAECC-18 '09 Proceedings of the 18th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
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We prove an upper bound on the covering radius of linear codes over IFq in terms of their generalized Hamming weights. We show that this bound is strengthened if we know that the codes satisfy the chain condition or a partial chain condition. We show that this bound improves all prior bounds. Necessary conditions for equality are also presented. Several applications of our bound are presented. We give tables of improved bounds on the covering radius of many cyclic codes using their generalized Hamming weights. We show that most cyclic codes of length ≤ 39 satisfy the chain condition or partial chain condition up to level 5. We use these results to derive tighter bounds on the covering radius of cyclic codes.