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On the non-minimality of the largest weight codewords in the binary Reed-Muller codes
1. | Department of Mathematics, Ghent University, Krijgslaan 281 - S22, 9000 Ghent, Belgium, Belgium |
References:
[1] |
A. Ashikhmin and A. Barg, Minimal vectors in linear codes,, IEEE Trans. Inform. Theory, 44 (1998), 2010.
doi: 10.1109/18.705584. |
[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.
doi: 10.1016/S0166-218X(02)00436-5. |
[3] |
T. Kasami and N. Tokura, On the weight structure of Reed-Muller codes,, IEEE Trans. Inform. Theory, IT-16 (1970), 752.
doi: 10.1109/TIT.1970.1054545. |
[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., (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.
doi: 10.1016/S0019-9958(76)90355-7. |
[6] |
F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'', North-Holland, (1977). Google Scholar |
[7] |
J. L. Massey, Minimal codewords and secret sharing,, in, (1993), 276. Google Scholar |
[8] |
J. Schillewaert, L. Storme and J. A. Thas, Minimal codewords in Reed-Muller codes,, Des. Codes Crypt., 54 (2010), 273.
doi: 10.1007/s10623-009-9323-x. |
show all references
References:
[1] |
A. Ashikhmin and A. Barg, Minimal vectors in linear codes,, IEEE Trans. Inform. Theory, 44 (1998), 2010.
doi: 10.1109/18.705584. |
[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.
doi: 10.1016/S0166-218X(02)00436-5. |
[3] |
T. Kasami and N. Tokura, On the weight structure of Reed-Muller codes,, IEEE Trans. Inform. Theory, IT-16 (1970), 752.
doi: 10.1109/TIT.1970.1054545. |
[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., (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.
doi: 10.1016/S0019-9958(76)90355-7. |
[6] |
F. J. MacWilliams and N. J. A. Sloane, "The Theory of Error-Correcting Codes,'', North-Holland, (1977). Google Scholar |
[7] |
J. L. Massey, Minimal codewords and secret sharing,, in, (1993), 276. Google Scholar |
[8] |
J. Schillewaert, L. Storme and J. A. Thas, Minimal codewords in Reed-Muller codes,, Des. Codes Crypt., 54 (2010), 273.
doi: 10.1007/s10623-009-9323-x. |
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