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Extremal Type I additive self-dual codes over $GF(4)$ with near-minimal shadow
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In this paper, we define near-minimal shadow and study the existence problem of extremal Type I additive self-dual codes over $GF(4)$ with near-minimal shadow. We prove that there is no such codes if the code length $n = 6m+1 (m \geq 0)$, $n = 6m+5 (m \geq 1)$.
Abstract
In this paper, we define near-minimal shadow and study the existence problem of extremal Type I additive self-dual codes over $GF(4)$ with near-minimal shadow. We prove that there is no such codes if the code length $n = 6m+1 (m \geq 0)$, $n = 6m+5 (m \geq 1)$.
참고문헌 (9)
- E. P. Bautista, "s-extremal additive codes", Adv. Math. Commun, 1, pp.111~130 (2007)
- W. Bosma, "The Magma algebra system I : The user language", J. Symbolic Comput, 24, pp.235~265 (1997)
- P. Gaborit, "Codes and Association Schemes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science 56", pp.135~149 (2001), American Mathematical Society
- S. Han, "Additive self-dual codes over GF(4)with minimal shadow", MDPI Information, 9(81), pp.1~11 (2018)
- S. Han, "Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2)and GF(4)", MDPI Information, 9(172), pp.1~12 (2018)
- S. Han, "On the extremal Type I binary self-dual codes with near-minimal shadow", ~
- G. Hhn, "Self-dual codes over the Kleinian four group", Math. Ann, 327, pp.227~255 (2003)
- W. C. Huffman, "On the classi cation and enumeration of self-dual codes", Finite Fields Appl, 11, pp.451~490 (2005)
- E. M. Rains, "Shadow bounds for self-dual codes", IEEE Trans. Inform. Theory, 44, pp.134~139 (1998)
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