Cyclic Codes from Some Monomials and Trinomials

DOI10.1137/120882275zbMath1306.94114OpenAlexW1999918393MaRDI QIDQ5408604

Cunsheng Ding

Publication date: 10 April 2014

Published in: SIAM Journal on Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/120882275

zbMATH Keywords

sequencespolynomialscyclic codespermutation polynomialslinear span

Mathematics Subject Classification ID

Algebraic coding theory; cryptography (number-theoretic aspects) (11T71) Linear codes (general theory) (94B05) Polynomials over finite fields (11T06) Cyclic codes (94B15)

Related Items (31)

Constructing new APN functions and bent functions over finite fields of odd characteristic via the switching method ⋮ A survey on the applications of Niho exponents ⋮ New classes of permutation binomials and permutation trinomials over finite fields ⋮ New permutation trinomials constructed from fractional polynomials ⋮ New constructions of permutation polynomials of the form \(x^rh\left( x^{q-1}\right) \) over \({\mathbb F}_{q^2}\) ⋮ Six New Classes of Permutation Trinomials over $\mathbb{F}_{2^{n}}$ ⋮ New constructions of involutions over finite fields ⋮ Binary cyclic codes from explicit polynomials over \(\mathrm{GF}(2^m)\) ⋮ Dembowski-Ostrom polynomials from reversed Dickson polynomials ⋮ On the inverses of some classes of permutations of finite fields ⋮ On the Ding and Helleseth's 7th open problem about optimal ternary cyclic codes ⋮ Some \(q\)-ary cyclic codes from explicit monomials over \(\mathbb{F}_{q^m}\) ⋮ A general construction of regular complete permutation polynomials ⋮ A new class of distance-optimal binary cyclic codes and their duals ⋮ Expressing the minimum distance, weight distribution and covering radius of codes by means of the algebraic and numerical normal forms of their indicators ⋮ Compositional inverses of AGW-PPs -- dedicated to Professor Cunsheng Ding for his 60th birthday ⋮ A class of optimal ternary cyclic codes and their duals ⋮ Permutation polynomials and their compositional inverses over finite fields by a local method ⋮ Constructing permutation polynomials over \(\mathbb{F}_{q^3}\) from bijections \(\mathrm{PG}(2,q)\) ⋮ A sequence construction of cyclic codes over finite fields ⋮ Generalized Lucas polynomials over finite fields ⋮ Further results on optimal ternary cyclic codes ⋮ New classes of optimal ternary cyclic codes with minimum distance four ⋮ Some cyclic codes from some monomials ⋮ Compositional inverses and complete mappings over finite fields ⋮ Recent results and problems on constructions of linear codes from cryptographic functions ⋮ Extended framework for constructing (complete) permutations by specifying their coordinate functions ⋮ On some conjectures about optimal ternary cyclic codes ⋮ A note on cyclic codes from APN functions ⋮ A link between two classes of permutation polynomials ⋮ On an open problem about a class of optimal ternary cyclic codes

This page was built for publication: Cyclic Codes from Some Monomials and Trinomials