The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
선형 코드의 갈루아 껍질(Galois hull)은 코드와 갈루아 쌍대(Galois Dual)의 교차점으로 정의됩니다. 본 논문에서는 F에 대한 순환 코드의 Galois 껍질을 조사합니다.qr. 임의의 정수에 대해 s≤r, 순환코드가 갖는 충분조건과 필요조건을 제시한다. l차원 s- 갈루아 선체. 또한, 우리는 순환 코드임을 증명합니다. C 이 l차원 s-갈루아 선체 iff C 이 l-차원 (r-s)-갈루아 선체. 특히, 1차원 갈루아 선체를 갖는 순환 코드에 대한 충분조건과 필요 조건, 그리고 1차원 갈루아 선체를 갖는 순환 코드와 갈루아 상보 이중성을 갖는 순환 코드 간의 관계를 제시합니다. Galois 선체를 사용하는 일부 최적의 순환 코드가 얻어집니다. 마지막으로 F에 대한 1-갈루아 선형 상보 이중을 사용하여 순환 코드 클래스를 명시적으로 구성합니다.q3.
Yang DING
Shanghai University
Xiaohua LU
Shanghai University
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부
Yang DING, Xiaohua LU, "Galois Hulls of Cyclic Codes over Finite Fields" in IEICE TRANSACTIONS on Fundamentals,
vol. E103-A, no. 1, pp. 370-375, January 2020, doi: 10.1587/transfun.2019EAL2087.
Abstract: The Galois hull of linear code is defined to be the intersection of the code and its Galois dual. In this paper, we investigate the Galois hulls of cyclic codes over Fqr. For any integer s≤r, we present some sufficient and necessary conditions that cyclic codes have l-dimensional s-Galois hull. Moreover, we prove that a cyclic code C has l-dimensional s-Galois hull iff C has l-dimensional (r-s)-Galois hull. In particular, we also present the sufficient and necessary condition for cyclic codes with 1-dimensional Galois hulls and the relationship between cyclic codes with 1-dimensional Galois hulls and cyclic codes with Galois complementary duals. Some optimal cyclic codes with Galois hulls are obtained. Finally, we explicitly construct a class of cyclic codes with 1-Galois linear complementary dual over Fq3.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2019EAL2087/_p
부
@ARTICLE{e103-a_1_370,
author={Yang DING, Xiaohua LU, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Galois Hulls of Cyclic Codes over Finite Fields},
year={2020},
volume={E103-A},
number={1},
pages={370-375},
abstract={The Galois hull of linear code is defined to be the intersection of the code and its Galois dual. In this paper, we investigate the Galois hulls of cyclic codes over Fqr. For any integer s≤r, we present some sufficient and necessary conditions that cyclic codes have l-dimensional s-Galois hull. Moreover, we prove that a cyclic code C has l-dimensional s-Galois hull iff C has l-dimensional (r-s)-Galois hull. In particular, we also present the sufficient and necessary condition for cyclic codes with 1-dimensional Galois hulls and the relationship between cyclic codes with 1-dimensional Galois hulls and cyclic codes with Galois complementary duals. Some optimal cyclic codes with Galois hulls are obtained. Finally, we explicitly construct a class of cyclic codes with 1-Galois linear complementary dual over Fq3.},
keywords={},
doi={10.1587/transfun.2019EAL2087},
ISSN={1745-1337},
month={January},}
부
TY - JOUR
TI - Galois Hulls of Cyclic Codes over Finite Fields
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 370
EP - 375
AU - Yang DING
AU - Xiaohua LU
PY - 2020
DO - 10.1587/transfun.2019EAL2087
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E103-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2020
AB - The Galois hull of linear code is defined to be the intersection of the code and its Galois dual. In this paper, we investigate the Galois hulls of cyclic codes over Fqr. For any integer s≤r, we present some sufficient and necessary conditions that cyclic codes have l-dimensional s-Galois hull. Moreover, we prove that a cyclic code C has l-dimensional s-Galois hull iff C has l-dimensional (r-s)-Galois hull. In particular, we also present the sufficient and necessary condition for cyclic codes with 1-dimensional Galois hulls and the relationship between cyclic codes with 1-dimensional Galois hulls and cyclic codes with Galois complementary duals. Some optimal cyclic codes with Galois hulls are obtained. Finally, we explicitly construct a class of cyclic codes with 1-Galois linear complementary dual over Fq3.
ER -