The New Minimum Distance Bounds of Goppa Codes and Their Decoding
Designs, Codes and Cryptography
On the Minimum Distances of Non-Binary Cyclic Codes
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Discrete Fourier Transform and Gröbner Bases
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Jack van Lint (1932-2004): a survey of his scientific work
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
A symmetric Roos bound for linear codes
Journal of Combinatorial Theory Series A - Special issue in honor of Jacobus H. van Lint
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
On the covering radius of certain cyclic codes
AAECC'03 Proceedings of the 15th international conference on Applied algebra, algebraic algorithms and error-correcting codes
The weight distributions of cyclic codes with two zeros and zeta functions
Journal of Symbolic Computation
On the triple-error-correcting cyclic codes with zero set {1, 2i + 1, 2i + 1}
IMACC'11 Proceedings of the 13th IMA international conference on Cryptography and Coding
APN monomials over GF(2n ) for infinitely many n
Finite Fields and Their Applications
Coset bounds for algebraic geometric codes
Finite Fields and Their Applications
Description of Minimum Weight Codewords of Cyclic Codes by Algebraic Systems
Finite Fields and Their Applications
On three weights in cyclic codes with two zeros
Finite Fields and Their Applications
A Proof of the Welch and Niho Conjectures on Cross-Correlations of Binary m-Sequences
Finite Fields and Their Applications
A new bound on the minimum distance of cyclic codes using small-minimum-distance cyclic codes
Designs, Codes and Cryptography
| Hi-index | 754.84 |
The main result is a new lower bound for the minimum distance of cyclic codes that includes earlier bounds (i.e., BCH bound, HT bound, Roos bound). This bound is related to a second method for bounding the minimum distance of a cyclic code, which we call shifting. This method can be even stronger than the first one. For all binary cyclic codes of length< 63(with two exceptions), we show that our methods yield the true minimum distance. The two exceptions at the end of our list are a code and its even-weight subcode. We treat several examples of cyclic codes of lengthgeq 63.