Bent Vectorial Functions, Codes and Designs

被引：20

作者：

Ding, Cunsheng ^{[1
]}

Munemasa, Akihiro ^{[2
]}

Tonchev, Vladimir D. ^{[3
]}

机构：

[1] Hong Kong Univ Sci & Technol, Dept Comp Sci & Engn, Hong Kong, Peoples R China

[2] Tohoku Univ, Grad Sch Informat Sci, Res Ctr Pure & Appl Math, Sendai, Miyagi 9808579, Japan

[3] Michigan Technol Univ, Dept Math Sci, Houghton, MI 49931 USA

来源：

IEEE TRANSACTIONS ON INFORMATION THEORY | 2019年 / 65卷 / 11期

关键词：

Bent function; bent vectorial function; linear code; 2-design; QUASI-SYMMETRICAL DESIGNS; BOOLEAN FUNCTIONS; RANKS;

D O I：

10.1109/TIT.2019.2922401

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group (GF(2(2m)),+), have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective of this paper is to use bent vectorial functions for a construction of a two-parameter family of binary linear codes that do not satisfy the conditions of the Assmus-Mattson theorem, but nevertheless hold 2-designs. A new coding-theoretic characterization of bent vectorial functions is presented.

引用

页码：7533 / 7541

页数：9

共 25 条

[1] Assmus E. F. Jr., 1969, Journal of Combinatorial Theory, Series A, V6, P122, DOI 10.1016/S0021-9800(69)80115-8
[2] Assmus Jr E.F., 1992, Designs and their Codes
[3] Beth T., 1999, Encyclopedia of Mathematics and its Applications
[4] On Boolean functions with the sum of every two of them being bent
Bey, Christian
Kyureghyan, Gohar M.
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2008, 49 (1-3) : 341 - 346
[5] The Magma algebra system .1. The user language
Bosma, W
Cannon, J
Playoust, C
[J]. JOURNAL OF SYMBOLIC COMPUTATION, 1997, 24 (3-4) : 235 - 265
[6] Carlet Claude, 2010, International Journal of Information and Coding Theory, V1, P133, DOI 10.1504/IJICOT.2010.032131
[7] Four decades of research on bent functions
Carlet, Claude
Mesnager, Sihem
[J]. DESIGNS CODES AND CRYPTOGRAPHY, 2016, 78 (01) : 5 - 50
[8] Dillion J.F., 1987, P NSA MATH SCI M, P159
[9] Parameters of 2-Designs from Some BCH Codes
Ding, Cunsheng
Zhou, Zhengchun
[J]. CODES, CRYPTOLOGY AND INFORMATION SECURITY, C2SI 2017, 2017, 10194 : 110 - 127
[10] Grassl M., CODE TABLES

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