Korean J. Math.  Vol 26, No 4 (2018)  pp.729-740
DOI: https://doi.org/10.11568/kjm.2018.26.4.729

Extremal Type I additive self-dual codes over $GF(4)$ with near-minimal shadow

Sunghyu Han

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 $n = 6m+1 (m \geq 0)$, $n = 6m+5 (m \geq 1)$.


Keywords


additive codes over $GF(4)$; extremal codes; minimal shadow; near-minimal shadow; self-dual codes

Subject classification

94B05

Sponsor(s)



Full Text:

PDF

References


E.P. Bautista, P. Gaborit, J.-L. Kim, J.L. Walker, s-extremal additive codes, Adv. Math. Commun. 1 (2007), 111–130. (Google Scholar)

W. Bosma, J. Cannon, C. Playoust, The Magma algebra system I: The user language, J. Symbolic Comput. 24 (1997), 235–265. (Google Scholar)

P. Gaborit, W.C. Huffman, J.-L. Kim, V. Pless, On additive GF(4) codes, in: A. Barg, S. Litsyn (Eds.), Codes and Association Schemes, DIMACS Series in Discrete Mathematics and Theoretical Computer Science, 56, American Mathematical Society, Providence, RI, 2001, 135–149. (Google Scholar)

S. Han, Additive self-dual codes over GF(4) with minimal shadow, MDPI Information 9 81 (2018), 1-11. (Google Scholar)

S. Han, Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4), MDPI Information 9 172 (2018), 1-12. (Google Scholar)

S. Han, On the extremal Type I binary self-dual codes with near-minimal shadow, submitted. (Google Scholar)

G. Höhn, Self-dual codes over the Kleinian four group, Math. Ann. 327 (2003), 227–255. (Google Scholar)

W.C. Huffman, On the classification and enumeration of self-dual codes, Finite Fields Appl. 11 (2005), 451-490. (Google Scholar)

E.M. Rains, Shadow bounds for self-dual codes, IEEE Trans. Inform. Theory 44 (1998), 134-139. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr