Self-dual and self-orthogonal negacyclic codes of length<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:msup><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>m</mml:mi></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>n</mml:mi></mml:mrow></mml:msup></mml:math>over a finite field

Sharma, Anuradha

doi:10.1016/j.disc.2014.11.008

Cited by 11 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using those characterizations, we obtain infinite families of p-ary LCD codes and self-orthogonal codes from the proposed linear codes and their duals. To our best knowledge, the self-orthogonal codes constructed in this paper have different parameters from that of those selforthogonal codes constructed in other literature [30,32,35]. Until now, people can only determine the weight distribution of a few class of self-orthogonal codes.…”

Section: Introductionmentioning

confidence: 97%

Some classes of LCD codes and self-orthogonal codes over finite fields

Li¹,

Cheng²,

Tang³

et al. 2019

Advances in Mathematics of Communications

View full text Add to dashboard Cite

Due to their important applications in theory and practice, linear complementary dual (LCD) codes and self-orthogonal codes have received much attention in the last decade. The objective of this paper is to extend a recent construction of binary LCD codes and self-orthogonal codes to the general pary case, where p is an odd prime. Based on the extended construction, several classes of p-ary linear codes are obtained. The characterizations of these linear codes to be LCD or self-orthogonal are derived. The duals of these linear codes are also studied. It turns out that the proposed linear codes are optimal in many cases in the sense that their parameters meet certain bounds on linear codes. The weight distributions of these linear codes are settled.

show abstract

Section: Introductionmentioning

confidence: 97%

Some classes of LCD codes and self-orthogonal codes over finite fields

Li¹,

Cheng²,

Tang³

et al. 2019

Advances in Mathematics of Communications

View full text Add to dashboard Cite

show abstract

“…In a series of papers, Dinh [6,7,8]determined the generator polynomials of all constacyclic codes of length ap s over F q and their duals, where a ∈ {2, 3, 6}. In the meanwhile, the generator polynomials of constacyclic codes of length 2 t p s over F q were obtained in [1,10,14], where q is a power of the prime p. In 2014, Chen et al [3] studied the structure of constacyclic codes of length lp s over F q and their duals in terms of their generator polynomials, where l is a prime different from p. All self-dual and linear complementary dual constacyclic codes were also obtained. Sharma [15] characterized all constacyclic codes of length l t p s over F q and their duals, where l and p are distinct primes, l is odd, s and t are positive integers.…”

Section: Introductionmentioning

confidence: 99%

Repeated-root constacyclic codes of length 6lmpn

Wu¹,

Zhu²,

Liu³

et al. 2023

AMC

View full text Add to dashboard Cite

Let <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula> be a finite field with character <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>. In this paper, the multiplicative group <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_{q}^{*} = \mathbb{F}_{q}\setminus\{0\} $\end{document}</tex-math></inline-formula> is decomposed into a mutually disjoint union of <inline-formula><tex-math id="M4">\begin{document}$ \gcd(6l^mp^n,q-1) $\end{document}</tex-math></inline-formula> cosets over subgroup <inline-formula><tex-math id="M5">\begin{document}$ <\xi^{6l^mp^n}> $\end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id="M6">\begin{document}$ \xi $\end{document}</tex-math></inline-formula> is a primitive element of <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula>. Based on the decomposition, the structure of constacyclic codes of length <inline-formula><tex-math id="M8">\begin{document}$ 6l^mp^n $\end{document}</tex-math></inline-formula> over finite field <inline-formula><tex-math id="M9">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula> and their duals is established in terms of their generator polynomials, where <inline-formula><tex-math id="M10">\begin{document}$ p\neq{3} $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M11">\begin{document}$ l\neq{3} $\end{document}</tex-math></inline-formula> are distinct odd primes, <inline-formula><tex-math id="M12">\begin{document}$ m $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M13">\begin{document}$ n $\end{document}</tex-math></inline-formula> are positive integers. In addition, we determine the characterization and enumeration of all linear complementary dual(LCD) negacyclic codes and self-dual constacyclic codes of length <inline-formula><tex-math id="M14">\begin{document}$ 6l^mp^n $\end{document}</tex-math></inline-formula> over <inline-formula><tex-math id="M15">\begin{document}$ \mathbb{F}_{q} $\end{document}</tex-math></inline-formula>.

show abstract

“…In Ref. [10], Sharma determined all self-dual and self-orthogonal negacyclic codes of length 2p e l m over the finite field F q , where gcd(p, q) = gcd(l, q) = 1. Much work has been done on the construction of self-orthogonal negacyclic codes, while the Hamming distances of negacyclic codes have been seldom discussed.…”

Section: Introductionmentioning

confidence: 99%

The Hamming Distances of a Class of p ‐Ary Negacyclic Codes

Ding

2018

Chin. j. electron.

View full text Add to dashboard Cite

Self-dual and self-orthogonal negacyclic codes of length2mpnover a finite field

Cited by 11 publications

References 20 publications

Some classes of LCD codes and self-orthogonal codes over finite fields

Some classes of LCD codes and self-orthogonal codes over finite fields

Repeated-root constacyclic codes of length 6<i>l<sup>m</sup>p<sup>n</sup></i>

The Hamming Distances of a Class of p ‐Ary Negacyclic Codes

Contact Info

Product

Resources

About