Bounds on the Covering Radius of Linear Codes
Designs, Codes and Cryptography
Good expander graphs and expander codes: parameters and decoding
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
| Hi-index | 754.84 |
Tietaivainen (1991) derived an upper bound on the covering radius of codes as a function of the dual distance. This was generalized to the minimum distance, and to Q-polynomial association schemes by Levenshtein and Fazekas. Both proofs use a linear programming approach. In particular, Levenshtein and Fazekas (1990) use linear programming bounds for codes and designs. In this article, proofs relying solely on the orthogonality relations of Krawtchouk (1929), Lloyd, and, more generally, Krawtchouk-adjacent orthogonal polynomials are derived. As a by-product upper bounds on the minimum distance of formally self-dual binary codes are derived