Several classes of optimal ternary cyclic codes with minimal distance four

DOI10.1016/j.ffa.2016.03.007zbMath1405.94126OpenAlexW2342825903MaRDI QIDQ285469

Gaofei Wu, Lisha Wang

Publication date: 19 May 2016

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

Full work available at URL: https://doi.org/10.1016/j.ffa.2016.03.007

zbMATH Keywords

linear codescyclic codesoptimal codessphere packing bound

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Cyclic codes (94B15) Applications of the theory of convex sets and geometry of numbers (covering radius, etc.) to coding theory (94B75)

Related Items (13)

A family of optimal ternary cyclic codes with minimum distance five and their duals ⋮ Two families of optimal ternary cyclic codes with minimal distance four ⋮ A family of cyclic codes with two zeros ⋮ Several classes of optimal \(p\)-ary cyclic codes with minimum distance four ⋮ Two classes of cyclic extended double-error-correcting Goppa codes ⋮ Optimal \(p\)-ary cyclic codes with two zeros ⋮ 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 ⋮ New classes of optimal ternary cyclic codes with minimum distance four ⋮ On some conjectures about optimal ternary cyclic codes ⋮ On some conjectures about optimal ternary cyclic codes ⋮ On an open problem about a class of optimal ternary cyclic codes

Cites Work

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• 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 \(q\)-polynomial approach to cyclic codes
• A class of three-weight cyclic codes
• The Weight Distributions of Several Classes of Cyclic Codes From APN Monomials
• Linear Codes From Perfect Nonlinear Mappings and Their Secret Sharing Schemes
• Fundamentals of Error-Correcting Codes
• On Self-Dual Cyclic Codes Over Finite Fields
• Cyclic decoding procedures for Bose- Chaudhuri-Hocquenghem codes
• Five Families of Three-Weight Ternary Cyclic Codes and Their Duals
• A Family of Five-Weight Cyclic Codes and Their Weight Enumerators
• Optimal Ternary Cyclic Codes From Monomials
• On decoding BCH codes

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