Papers by Ekkasit Sangwisut
arXiv (Cornell University), Jan 2, 2016
Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algor... more Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing x n − λ over F q 2 is given, where λ is a unit in F q 2. Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over F q 2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dual) codes of length n over F q 2 are given through their Hermitian hulls. Subsequently, a new family of MDS constacyclic Hermitian self-dual codes over F q 2 is introduced. As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of x n − λ and the Chinese Remainder Theorem, quasi-twisted codes can be viewed as a product of linear codes of shorter length some over extension fields of F q 2. Necessary and sufficient conditions for quasi-twisted codes to be Hermitian self-dual are given. The enumeration of such self-dual codes is determined as well.
arXiv (Cornell University), Feb 1, 2017
The hulls of linear and cyclic codes have been extensively studied due to their wide applications... more The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field F q 2 is determined together with some upper and lower bounds. It turns out that either the average dimension of the Hermitian hull of constacyclic codes of length n over F q 2 is zero or it grows the same rate as n. Comparison to the average dimension of the Euclidean hull of cyclic codes is discussed as well.
The average dimension of the Hermitian hull of cyclic codes over finite fields of square order
AIP Conference Proceedings, 2016
In this paper, the average dimension of the Hermitian hull of cyclic codes of length n over Fq2, ... more In this paper, the average dimension of the Hermitian hull of cyclic codes of length n over Fq2, denoted by EH (n, q2), is studied. Some upper and lower bounds of EH (n, q2) are given. Moreover, EH (n, q2) is shown to be zero if and only if n ∈ Mq:={l≥1| l divides qi+1 for some odd positive integer i} and it grows the same rate as n if n ∉ Mq
In this paper, we study cyclic codes over the Galois ring ${\rm GR}({p^2},s)$. The main result is... more In this paper, we study cyclic codes over the Galois ring ${\rm GR}({p^2},s)$. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length $p^a$ over ${\rm GR}({p^2},s)$. Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over ${\rm GR}({p^2},s)$. Some corrections to results on Euclidean self-dual cyclic codes of even length over $\mathbb{Z}_4$ in Discrete Appl. Math. 128, (2003), 27 and Des. Codes Cryptogr. 39, (2006), 127 are provided.
Hulls of cyclic and negacyclic codes over finite fields
Finite Fields and Their Applications, 2015
ABSTRACT We study the hulls of cyclic and negacyclic codes of length n over a finite field with r... more ABSTRACT We study the hulls of cyclic and negacyclic codes of length n over a finite field with respect to the Euclidean and Hermitian inner products. Based on the characterization of their generator polynomials, the dimensions of the hulls of cyclic and negacyclic codes of length n over are determined. The enumerations of cyclic codes and negacyclic codes of length n over having hulls of a given dimension are established as well. As special cases, known results concerning complementary dual and self-dual cyclic codes can be viewed as corollaries of results in this paper.
The Group of Primitive Pythagorean Triples and Perplex Numbers
Mathematics Magazine
Hulls of Cyclic Codes over the Ring F2 + vF2
Thai Journal of Mathematics, 2021
Advances in Mathematics of Communications, 2016
In this paper, cyclic codes over the Galois ring GR(p 2 , s) are studied. The main result is the ... more In this paper, cyclic codes over the Galois ring GR(p 2 , s) are studied. The main result is the characterization and enumeration of Hermitian self-dual cyclic codes of length p a over GR(p 2 , s). Combining with some known results and the standard Discrete Fourier Transform decomposition, we arrive at the characterization and enumeration of Euclidean self-dual cyclic codes of any length over GR(p 2 , s).
The Group of Primitive Pythagorean Triples Over Gaussian Integers
SSRN Electronic Journal
The hulls of linear and cyclic codes over finite fields have been of interest and extensively stu... more The hulls of linear and cyclic codes over finite fields have been of interest and extensively studied due to their wide applications. In this paper, the hulls of cyclic codes of length $n$ over the ring $\mathbb{Z}_4$ have been focused on. Their characterization has been established in terms of the generators viewed as ideals in the quotient ring $\mathbb{Z}_4[x]/\langle x^n-1\rangle$. An algorithm for computing the types of the hulls of cyclic codes of arbitrary odd length over $\mathbb{Z}_4$ has been given. The average $2$-dimension $E(n)$ of the hulls of cyclic codes of odd length $n$ over $\mathbb{Z}_4$ has been established. A general formula for $E(n)$ has been provided together with its upper and lower bounds. It turns out that $E(n)$ grows the same rate as $n$.
The average dimension of the Hermitian hull of constacyclic codes over finite fields of square order
Advances in Mathematics of Communications
Hulls of cyclic codes over Z4
Discrete Mathematics
Mathematical and Computational Applications, Aug 20, 2018
Hulls of linear codes have been extensively studied due to their wide applications and links with... more Hulls of linear codes have been extensively studied due to their wide applications and links with the efficiency of some algorithms in coding theory. In this paper, the average dimension of the Euclidean hull of negacyclic codes of length n over finite fields F q , denoted by E(n, −1, q), has been investigated. The formula for E(n, −1, q) has been determined. Some upper and lower bounds of E(n, −1, q) have been given as well. Asymptotically, it has been shown that either E(n, −1, q) is zero or it grows the same rate as n.
Advances in Mathematics of Communications
Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algor... more Constacyclic and quasi-twisted Hermitian self-dual codes over finite fields are studied. An algorithm for factorizing x n − λ over F q 2 is given, where λ is a unit in F q 2. Based on this factorization, the dimensions of the Hermitian hulls of λ-constacyclic codes of length n over F q 2 are determined. The characterization and enumeration of constacyclic Hermitian self-dual (resp., complementary dual) codes of length n over F q 2 are given through their Hermitian hulls. Subsequently, a new family of MDS constacyclic Hermitian self-dual codes over F q 2 is introduced. As a generalization of constacyclic codes, quasi-twisted Hermitian self-dual codes are studied. Using the factorization of x n − λ and the Chinese Remainder Theorem, quasi-twisted codes can be viewed as a product of linear codes of shorter length some over extension fields of F q 2. Necessary and sufficient conditions for quasi-twisted codes to be Hermitian self-dual are given. The enumeration of such self-dual codes is determined as well.
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Papers by Ekkasit Sangwisut