New classes of optimal ternary cyclic codes with minimum distance four

DOI10.1016/J.FFA.2020.101671zbMath1434.94104OpenAlexW3013959785MaRDI QIDQ1987113

Lei Hu, Zhengbang Zha

Publication date: 9 April 2020

Published in: Finite Fields and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ffa.2020.101671

zbMATH Keywords

finite fieldscyclic codesirreducible polynomialssphere packing bound

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15)

Related Items (8)

A family of optimal ternary cyclic codes with minimum distance five and their duals ⋮ A family of cyclic codes with two zeros ⋮ Several classes of optimal \(p\)-ary cyclic codes with minimum distance four ⋮ On the Ding and Helleseth's 7th open problem about optimal ternary cyclic codes ⋮ Several new classes of optimal ternary cyclic codes with minimum distance four ⋮ Two classes of new optimal ternary cyclic codes ⋮ Further results on optimal ternary cyclic codes ⋮ On some conjectures about optimal ternary cyclic codes

Cites Work

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• The weight distribution of a class of \(p\)-ary cyclic codes
• A triple-error-correcting cyclic code from the Gold and Kasami-Welch APN power functions
• On cyclic codes of length \(2^{2^r}-1\) with two zeros whose dual codes have three weights
• A family of optimal ternary cyclic codes from the Niho-type exponent
• On an open problem about a class of optimal ternary cyclic codes
• A class of three-weight cyclic codes
• Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes
• Value Distributions of Exponential Sums From Perfect Nonlinear Functions and Their Applications
• Fundamentals of Error-Correcting Codes
• Optimal Ternary Cyclic Codes From Monomials
• Cyclic Codes from Some Monomials and Trinomials

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