Infinite families of 2-designs from two classes of binary cyclic codes with three nonzeros

DOI10.3934/amc.2020106zbMath1490.94075arXiv1903.08153OpenAlexW3064996342MaRDI QIDQ2070264

Rong Wang, Xiaoni Du, Qi Wang, Chun-Ming Tang

Publication date: 24 January 2022

Published in: Advances in Mathematics of Communications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.08153

zbMATH Keywords

2-designlinear codeweight distributioncyclic codeBCH codeaffine-invariant code

Mathematics Subject Classification ID

Combinatorial aspects of block designs (05B05) Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Cyclic codes (94B15)

Related Items (9)

Linear codes of 2-designs as subcodes of the generalized Reed-Muller codes ⋮ A class of affine-invariant codes and their support 2-designs ⋮ Some \(t\)-designs from BCH codes ⋮ Infinite families of \(t\)-designs and strongly regular graphs from punctured codes ⋮ Steiner systems \(S(2,4, 2^m)\) supported by a family of extended cyclic codes ⋮ Infinite Families of 2-Designs from a Class of Linear Codes Related to Dembowski-Ostrom Functions ⋮ New infinite families of near MDS codes holding \(t\)-designs ⋮ Combinatorial \(t\)-designs from quadratic functions ⋮ Linear codes from support designs of ternary cyclic codes

Cites Work

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• Infinite families of 2-designs and 3-designs from linear codes
• Infinite families of 3-designs from a type of five-weight code
• Designs from Linear Codes
• Cyclic Codes and Sequences: The Generalized Kasami Case
• Some results on cyclic codes which are invariant under the affine group and their applications
• New 5-designs

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