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Weierstrass semigroup and codes over the curve $y^q + y = x^{q^r + 1}$
Self-dual [62, 31, 12] and [64, 32, 12] codes with an automorphism of order 7
1. | Faculty of Mathematics and Informatics, Konstantin Preslavski University of Shumen, Shumen, 9712, Bulgaria |
References:
[1] |
I. Bouyukliev, About the code equivalence, in Advances in Coding Theory and Cryptography, World Scientific Publishing, 2007.
doi: 10.1142/9789812772022_0009. |
[2] |
S. Bouyuklieva, N. Yankov and J.-L. Kim, Classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order, Finite Fields Appl., 18 (2012), 1104-1113.
doi: 10.1016/j.ffa.2012.08.002. |
[3] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual codes having an automorphism of order 3, Finite Fields Appl., 13 (2007), 605-615.
doi: 10.1016/j.ffa.2006.01.001. |
[4] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual [44, 22, 8] codes with an automorphism of order 3 or 7, Int. J. Inform. Coding Theory, 2 (2011), 21-37.
doi: 10.1504/IJICOT.2011.044676. |
[5] |
N. Chigira, M. Harada and M. Kitazume, Extremal self-dual codes of length 64 through neighbors and covering radii, Des. Codes Crypt., 42 (2007), 93-101.
doi: 10.1007/s10623-006-9018-5. |
[6] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[7] |
W. C. Huffman, Automorphisms of codes with application to extremal doubly-even codes of length 48, IEEE Trans. Inform. Theory, 28 (1982), 511-521.
doi: 10.1109/TIT.1982.1056499. |
[8] |
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[9] |
W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003. |
[10] |
V. I. Iorgov, Doubly even extremal codes of length 64, Probl. Inform. Transm., 22 (1986), 277-284. |
[11] |
S. Karadeniz and B. Yildiz, Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$, Adv. Math. Commun., 6 (2012), 193-202.
doi: 10.3934/amc.2012.6.193. |
[12] |
G. Pasquier, A binary extremal doubly even self-dual code (64,32,12) obtained from an extended Reed-Solomon code over $F_{16}$, IEEE Trans. Inform. Theory, 27 (1981), 807-808.
doi: 10.1109/TIT.1981.1056421. |
[13] |
R. Russeva and N. Yankov, On Binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9, Des. Codes Crypt., 45 (2007), 335-346.
doi: 10.1007/s10623-007-9127-9. |
[14] |
N. Yankov, On binary self-dual codes of length 62 with an automorphism of order 7, Math. Educ. Math., 40 (2011), 223-228. |
[15] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inform. Theory, 56 (2011), 7498-7506.
doi: 10.1109/TIT.2011.2155619. |
[16] |
V. Yorgov, Binary self-dual codes with an automorphism of odd order (in Russian), Probl. Inform. Transm., 4 (1983), 13-24. |
show all references
References:
[1] |
I. Bouyukliev, About the code equivalence, in Advances in Coding Theory and Cryptography, World Scientific Publishing, 2007.
doi: 10.1142/9789812772022_0009. |
[2] |
S. Bouyuklieva, N. Yankov and J.-L. Kim, Classification of binary self-dual [48, 24, 10] codes with an automorphism of odd prime order, Finite Fields Appl., 18 (2012), 1104-1113.
doi: 10.1016/j.ffa.2012.08.002. |
[3] |
S. Bouyuklieva, N. Yankov and R. Russeva, Classification of the binary self-dual codes having an automorphism of order 3, Finite Fields Appl., 13 (2007), 605-615.
doi: 10.1016/j.ffa.2006.01.001. |
[4] |
S. Bouyuklieva, N. Yankov and R. Russeva, On the classication of binary self-dual [44, 22, 8] codes with an automorphism of order 3 or 7, Int. J. Inform. Coding Theory, 2 (2011), 21-37.
doi: 10.1504/IJICOT.2011.044676. |
[5] |
N. Chigira, M. Harada and M. Kitazume, Extremal self-dual codes of length 64 through neighbors and covering radii, Des. Codes Crypt., 42 (2007), 93-101.
doi: 10.1007/s10623-006-9018-5. |
[6] |
J. H. Conway and N. J. A. Sloane, A new upper bound on the minimal distance of self-dual codes, IEEE Trans. Inform. Theory, 36 (1990), 1319-1333.
doi: 10.1109/18.59931. |
[7] |
W. C. Huffman, Automorphisms of codes with application to extremal doubly-even codes of length 48, IEEE Trans. Inform. Theory, 28 (1982), 511-521.
doi: 10.1109/TIT.1982.1056499. |
[8] |
W. C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl., 11 (2005), 451-490.
doi: 10.1016/j.ffa.2005.05.012. |
[9] |
W. C. Huffman and V. Pless, Fundamentals of Error Correcting Codes, Cambridge University Press, 2003. |
[10] |
V. I. Iorgov, Doubly even extremal codes of length 64, Probl. Inform. Transm., 22 (1986), 277-284. |
[11] |
S. Karadeniz and B. Yildiz, Double-circulant and bordered-double-circulant constructions for self-dual codes over $R_2$, Adv. Math. Commun., 6 (2012), 193-202.
doi: 10.3934/amc.2012.6.193. |
[12] |
G. Pasquier, A binary extremal doubly even self-dual code (64,32,12) obtained from an extended Reed-Solomon code over $F_{16}$, IEEE Trans. Inform. Theory, 27 (1981), 807-808.
doi: 10.1109/TIT.1981.1056421. |
[13] |
R. Russeva and N. Yankov, On Binary self-dual codes of lengths 60, 62, 64 and 66 having an automorphism of order 9, Des. Codes Crypt., 45 (2007), 335-346.
doi: 10.1007/s10623-007-9127-9. |
[14] |
N. Yankov, On binary self-dual codes of length 62 with an automorphism of order 7, Math. Educ. Math., 40 (2011), 223-228. |
[15] |
N. Yankov and R. Russeva, Binary self-dual codes of lengths 52 to 60 with an automorphism of order 7 or 13, IEEE Trans. Inform. Theory, 56 (2011), 7498-7506.
doi: 10.1109/TIT.2011.2155619. |
[16] |
V. Yorgov, Binary self-dual codes with an automorphism of odd order (in Russian), Probl. Inform. Transm., 4 (1983), 13-24. |
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