On the non-minimality of the largest weight codewords in the binary Reed-Muller codes
Pages: 333 - 337, Volume 5, Issue 2, May 2011

doi:10.3934/amc.2011.5.333      Abstract        References        Full text (263.3K)           Related Articles

Andreas Klein - Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent, Belgium (email)
Leo Storme - Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent, Belgium (email)

1	A. Ashikhmin and A. Barg, Minimal vectors in linear codes, IEEE Trans. Inform. Theory, 44 (1998), 2010-2017.
2	Y. Borissov, N. L. Manev and S. Nikova, On the non-minimal codewords in binary Reed-Muller codes, Discrete Appl. Math., 128 (2003), 65-74.
3	T. Kasami and N. Tokura, On the weight structure of Reed-Muller codes, IEEE Trans. Inform. Theory, IT-16 (1970), 752-759.
4	T. Kasami, N. Tokura and S. Azumi, On the weight enumeration of weight less than $2.5d$ of Reed-Muller codes, Rept. of Faculty of Eng. Sci., Osaka Univ., Japan, 1974.
5	T. Kasami, N. Tokura and S. Azumi, On the weight enumeration of weight less than $2.5d$ of Reed-Muller codes, Inform. Control, 30 (1976), 380-395.
6	F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'' North-Holland, Amsterdam, 1977.
7	J. L. Massey, Minimal codewords and secret sharing, in "Proceedings of the 6th Joint Swedish-Russian International Workshop on Information Theory,'' (1993), 276-279.
8	J. Schillewaert, L. Storme and J. A. Thas, Minimal codewords in Reed-Muller codes, Des. Codes Crypt., 54 (2010), 273-286.

Go to top