SELF-DUAL CODES OVER THE RING F2m + uF2m + vF2m + uvF2m
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
We discuss self-dual codes over the ring R = F2m +uF2m + vF2m + uvF2m, u² = 0, v² = 0, uv = vu. We consider de nition of trace function and self-dual basis over the field F2m. We consider the Gray map and self-orthogonal basis to discuss some theoretical properties of self-dual and Type II codes over the ring R. Also we see how Lee weight and trace are related over the ring R for a self-dual basis.
Abstract
We discuss self-dual codes over the ring R = F2m +uF2m + vF2m + uvF2m, u² = 0, v² = 0, uv = vu. We consider de nition of trace function and self-dual basis over the field F2m. We consider the Gray map and self-orthogonal basis to discuss some theoretical properties of self-dual and Type II codes over the ring R. Also we see how Lee weight and trace are related over the ring R for a self-dual basis.
참고문헌 (15)
- E. Bannai, "Type II codes over <TEX>${\mathbb{F}}_2+u{\mathbb{F}}_2$<", TEX> and applications to Hermitian modular forms, 2003, 13~42
- K. Betsumiya, "Type II codes over <TEX>${\mathbb{F}}_{2m}+u{\mathbb{F}}_{2m}$<", TEX>, 2004, pp.275(1), 43~65
- A. Bonnecaze, "Cyclic codes and self-dual codes over <TEX>${\mathbb{F}}_2+u{\mathbb{F}}_2$<", TEX>, 1999, pp.45(4), 1250~1255
- J. H. Conway, "The binary self-dual codes of length up to 32 : a revised enumeration", Journal of Combinatorial Theory, Series A, 60(2), pp.183~195 (1992)[DOI]
- S. T. Dougherty, "Type II codes over <TEX>${\mathbb{F}}_2+u{\mathbb{F}}_2$<", TEX>, 1999, pp.45(1), 32~45
- J. Fields, "All self-dual <TEX>$\mathbb{Z}_4$<", TEX> codes of length 15 or less are known, 1997, 202~
- P. Gaborit, "Mass formulas for self-dual codes over <TEX>$\mathbb{Z}_4$<", TEX> and <TEX>${\mathbb{F}}_q+u{\mathbb{F}}_q$<, IEEE Transactions on Information Theory, pp.1996, 42(4)[DOI]
- W. C. Huffman, "Self-dual codes over <TEX>${\mathbb{F}}_2+u{\mathbb{F}}_2$<", TEX> with an automorphism of odd order, 2009, pp.15(3), 277~293
- "<u^2,v^2,uv-vu>$<", TEX>, 2015, pp.34, 161~175
- S. Ling, "Type II codes over <TEX>${\mathbb{F}}_4+u{\mathbb{F}}_4$<", TEX>, 2001, pp.22(7), 983~997
- F. J. MacWilliams, "The theory of error correcting codes" (1977), Elsevier
- C. L. Mallows, "An upper bound for self-dual codes", Information and Control, 22(2), pp.188~200 (1973)[DOI]
- "<u^k>$<", TEX>. Designs, 2015, pp.74(1), 1~13
- B. Yildiz, "Linear codes over <TEX>$\mathbb{F}_2$<", TEX> + <TEX>$u{\mathbb{F}}_2$<, TEX> + <TEX>$uv{\mathbb{F}}_2$<, pp.TEX>, Designs, Codes and Cryptography[DOI]
- B. Yildiz, "self-dual codes over <TEX>${\mathbb{F}}_2+u{\mathbb{F}}_2+v{\mathbb{F}}_2+uv{\mathbb{F}}_2$<", TEX>, 2010, pp.347(10), 1888~1894