A CLASS OF SUBFIELD CODES AND THEIR DUALS

被引：0

作者：

Huang, Junsong ^{[1
]}

Yan, Tongjiang ^{[1
]}

机构：

[1] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China

来源：

ADVANCES IN MATHEMATICS OF COMMUNICATIONS | 2025年

关键词：

Subfield codes; weight distribution; dual codes; almost optimal code; BINARY LINEAR CODES; CYCLIC CODES;

D O I：

10.3934/amc.2025005

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

. Recently, Xiang and Yin studied two families of subfield codes of linear codes over F2m , and determined the weight distribution of the linear C(2) = {((Trq/2 (ax2 + by2 + wy) + c) } where q = 2m. Motivated by this paper and other former contributions, we study the subfield codes of linear codes over Fpm and obtain the weight distribution of {( ) 1J1 C(p) = Trpm/p(axpk+1 + bx + uy) + w x,y is an element of Fpm : a, b, u is an element of Fpm , w is an element of Fp , which is a self-orthogonal p-divisible linear code. We also investigate the dual codes of C(p), whose parameters are obtained by the weight distribution of C(p), and they are almost optimal codes.

引用

页数：11

共 27 条

[1] Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA [J].

Abbott, B. P. ;

Abbott, R. ;

Abbott, T. D. ;

Abraham, S. ;

Acernese, F. ;

Ackley, K. ;

Adams, C. ;

Adya, V. B. ;

Affeldt, C. ;

Agathos, M. ;

Agatsuma, K. ;

Aggarwal, N. ;

Aguiar, O. D. ;

Aiello, L. ;

Ain, A. ;

Ajith, P. ;

Akutsu, T. ;

Allen, G. ;

Allocca, A. ;

Aloy, M. A. ;

Altin, P. A. ;

Amato, A. ;

Ananyeva, A. ;

Anderson, S. B. ;

Anderson, W. G. ;

Ando, M. ;

Angelova, S. V. ;

Antier, S. ;

Appert, S. ;

Arai, K. ;

Arai, Koya ;

Arai, Y. ;

Araki, S. ;

Araya, A. ;

Araya, M. C. ;

Areeda, J. S. ;

Arene, M. ;

Aritomi, N. ;

Arnaud, N. ;

Arun, K. G. ;

Ascenzi, S. ;

Ashton, G. ;

Aso, Y. ;

Aston, S. M. ;

Astone, P. ;

Aubin, F. ;

Aufmuth, P. ;

AultONeal, K. ;

Austin, C. ;

Avendano, V. .

LIVING REVIEWS IN RELATIVITY, 2020, 23 (01)

[2]

Cannon J., 2013, Handbook of Magma Functions

[3] Weight divisibility of cyclic codes, highly nonlinear functions on F2m, and crosscorrelation of maximum-length sequences [J].

Canteaut, A ;

Charpin, P ;

Dobbertin, H .

SIAM JOURNAL ON DISCRETE MATHEMATICS, 2000, 13 (01) :105-138

[4] Codes, Bent Functions and Permutations Suitable for DES-like Cryptosystems [J].

Carlet C. ;

Charpin P. ;

Zinoviev V. .

Designs, Codes and Cryptography, 1998, 15 (2) :125-156

[5]

Cary Huffman., 2003, Fundamentals of Error-Correcting Codes

[6]

Ding C., 2019, Designs from Linear Codes

[7] The Subfield Codes of Ovoid Codes [J].

Ding, Cunsheng ;

Heng, Ziling .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2019, 65 (08) :4715-4729

[8] A construction of binary linear codes from Boolean functions [J].

Ding, Cunsheng .

DISCRETE MATHEMATICS, 2016, 339 (09) :2288-2303

[9] Three-weight cyclic codes and their weight distributions [J].

Ding, Cunsheng ;

Li, Chunlei ;

Li, Nian ;

Zhou, Zhengchun .

DISCRETE MATHEMATICS, 2016, 339 (02) :415-427

[10] Linear Codes From Some 2-Designs [J].

Ding, Cunsheng .

IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (06) :3265-3275

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