The dimension and minimum distance of two classes of primitive BCH codes

DOI10.1016/j.ffa.2016.12.009zbMath1402.94100arXiv1603.07007OpenAlexW2304375173MaRDI QIDQ2396760

Cunsheng Ding, Zhengchun Zhou, Cui Ling Fan

Publication date: 24 May 2017

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

Full work available at URL: https://arxiv.org/abs/1603.07007

zbMATH Keywords

BCH codeslinear codesweight distributionweight enumeratorcyclic codessecret sharing

Mathematics Subject Classification ID

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

Related Items (34)

Explicit characterization of two classes of regular bent functions ⋮ Some binary BCH codes with length \(n = 2^m + 1\) ⋮ Quantum BCH codes with maximum designed distance ⋮ Dimensions of three types of BCH codes over \(\mathrm{GF}(q)\) ⋮ Binary linear codes from vectorial Boolean functions and their weight distribution ⋮ A class of negacyclic BCH codes and its application to quantum codes ⋮ A class of constacyclic BCH codes ⋮ Infinite families of 3-designs from a type of five-weight code ⋮ More results on hulls of some primitive binary and ternary BCH codes ⋮ The Minimum Distance of Some Narrow-Sense Primitive BCH Codes ⋮ Dimensions of nonbinary antiprimitive BCH codes and some conjectures ⋮ Three classes of BCH codes and their duals ⋮ Some new results on dimension and Bose distance for various classes of BCH codes ⋮ Two families of negacyclic BCH codes ⋮ Parameters of hulls of primitive binary narrow-sense BCH codes and their subcodes ⋮ Ternary primitive LCD BCH codes ⋮ The maximum designed distances of dual-containing non-primitive BCH codes ⋮ New classes of bent functions via the switching method ⋮ New quantum codes derived from a family of antiprimitive BCH codes ⋮ BCH cyclic codes ⋮ Several classes of bent functions over finite fields ⋮ Binary primitive LCD BCH codes ⋮ BCH Codes with Minimum Distance Proportional to Code Length ⋮ Five families of the narrow-sense primitive BCH codes over finite fields ⋮ A class of primitive BCH codes and their weight distribution ⋮ Parameters of 2-Designs from Some BCH Codes ⋮ On some cyclic codes of length \(\frac{q^{2m} - 1}{q + 1} \) ⋮ Infinite families of 2-designs and 3-designs from linear codes ⋮ Several infinite families of \(p\)-ary weakly regular bent functions ⋮ Parameters of LCD BCH codes with two lengths ⋮ A class of narrow-sense BCH codes over \(\mathbb{F}_q\) of length \(\frac{q^m-1}{2} \) ⋮ A family of optimal ternary cyclic codes from the Niho-type exponent ⋮ Parameters and characterizations of hulls of some projective narrow-sense BCH codes ⋮ The dual-containing primitive BCH codes with the maximum designed distance and their applications to quantum codes

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