논문KCI 등재
Nonexistence of some extremal self-dual codes
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Abstract
It is known that ifC is an [24m + 2 l;12m + l;d] self-dual binary linear code with 0 l < 11, then d 4m + 4. Wepresent a sucient condition for the nonexistence of extremal self-dual binary linear codes with d = 4 m + 4 ;l = 1 ;2;3;5. Fromthe sucient condition, we calculate m's which correspond to thenonexistence of some extremal self-dual binary linear codes. Inparticular, we prove that there are innitely many suchm's. Wealso give similar results for additive self-dual codes overGF(4) oflength n = 6 m + 1.
참고문헌 (4)
- "Quantum errorcorrection via codes overGF(4)", 44(4), pp.1369~1387 (1998)
- "A new upper bound on the minimal distanceof self -dual codes", pp.1333~ (1990)
- "On the classication and enumeration of self-dual codes", 11(3), pp.451~490 (2005)
- "The theory of error correcting codes", 91(1-3), pp.277~286 (1999)
관련 논문AI추천
Extremal Type I additive self-dual codes over $GF(4)$ with near-minimal shadow한성휴강원경기수학회 · 한국수학논문집2018 · 제26권 제4호Additive self-dual codes over fields of even order김종락, 이나리, Steven T. Dougherty대한수학회 · 대한수학회보2018 · 제55권 제2호Mass Formula of self-dual codes over Galois rings $GR(p^2,2)$최환혁강원경기수학회 · 한국수학논문집2016 · 제24권 제4호The classification of self-dual codes over Galois rings of length 4최환혁대한수학회 · 대한수학회보2018 · 제55권 제5호Self-dual codes over ${\mathbb Z}_{p^2}$ of small lengths박영호, 최환혁강원경기수학회 · 한국수학논문집2017 · 제25권 제3호Perfect Codes on Some Ordered Sets이재권대한수학회 · 대한수학회보2006 · 제43권 제2호
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