Weight enumerators of reducible cyclic codes and their dual codes

2019 ◽  
Vol 342 (3) ◽  
pp. 671-682 ◽  
Author(s):  
Yansheng Wu ◽  
Qin Yue ◽  
Xiaomeng Zhu ◽  
Shudi Yang
Keyword(s):  
Cyclic Codes ◽  
Dual Codes ◽  
Weight Enumerators

scholarly journals Extremal binary self-dual codes of lengths 64 and 66 from four-circulant constructions over F2+uF2

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 937-945 ◽  
Author(s):  
Suat Karadeniz ◽  
Bahattin Yildiz ◽  
Nuh Aydin
Keyword(s):  
Dual Codes ◽  
Weight Enumerators ◽  
Extension Method ◽  
Extremal Codes ◽  
New Codes ◽  
First Time

A classification of all four-circulant extremal codes of length 32 over F2 + uF2 is done by using four-circulant binary self-dual codes of length 32 of minimum weights 6 and 8. As Gray images of these codes, a substantial number of extremal binary self-dual codes of length 64 are obtained. In particular a new code with ?=80 in W64,2 is found. Then applying an extension method from the literature to extremal self-dual codes of length 64, we have found many extremal binary self-dual codes of length 66. Among those, five of them are new codes in the sense that codes with these weight enumerators are constructed for the first time. These codes have the values ?=1, 30, 34, 84, 94 in W66,1.

scholarly journals Constacyclic and Linear Complementary Dual Codes Over Fq + uFq

2020 ◽  
Vol 70 (6) ◽  
pp. 626-632
Author(s):  
Om Prakash ◽  
Shikha Yadav ◽  
Ram Krishna Verma
Keyword(s):  
Cyclic Codes ◽  
Gray Map ◽  
Constacyclic Codes ◽  
Dual Codes ◽  
Gray Image ◽  
New Class ◽  
Sharing Scheme ◽  
Lcd Codes ◽  
Reversible Cyclic Codes

This article discusses linear complementary dual (LCD) codes over ℜ = Fq+uFq(u2=1) where q is a power of an odd prime p. Authors come up with a new Gray map from ℜn to F2nq and define a new class of codes obtained as the gray image of constacyclic codes over .ℜ Further, we extend the study over Euclidean and Hermitian LCD codes and establish a relation between reversible cyclic codes and Euclidean LCD cyclic codes over ℜ. Finally, an application of LCD codes in multisecret sharing scheme is given.

scholarly journals Self-Dual Abelian Codes in Some Nonprincipal Ideal Group Algebras

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Parinyawat Choosuwan ◽  
Somphong Jitman ◽  
Patanee Udomkavanich
Keyword(s):  
Cyclic Codes ◽  
Group Algebras ◽  
Dual Codes ◽  
Complete Enumeration ◽  
Odd Order ◽  
Abelian Codes ◽  
Positive Integers ◽  
Ideal Group ◽  
Suitable Product

The main focus of this paper is the complete enumeration of self-dual abelian codes in nonprincipal ideal group algebrasF2k[A×Z2×Z2s]with respect to both the Euclidean and Hermitian inner products, wherekandsare positive integers andAis an abelian group of odd order. Based on the well-known characterization of Euclidean and Hermitian self-dual abelian codes, we show that such enumeration can be obtained in terms of a suitable product of the number of cyclic codes, the number of Euclidean self-dual cyclic codes, and the number of Hermitian self-dual cyclic codes of length2sover some Galois extensions of the ringF2k+uF2k, whereu2=0. Subsequently, general results on the characterization and enumeration of cyclic codes and self-dual codes of lengthpsoverFpk+uFpkare given. Combining these results, the complete enumeration of self-dual abelian codes inF2k[A×Z2×Z2s]is therefore obtained.

scholarly journals Lee weight enumerators of self-dual codes and theta functions

2008 ◽  
Vol 2 (4) ◽  
pp. 393-402 ◽  
Author(s):  
Bram van Asch ◽  
◽  
Frans Martens
Keyword(s):  
Theta Functions ◽  
Dual Codes ◽  
Weight Enumerators ◽  
Lee Weight

scholarly journals Type IV codes over a non-unital ring

2021 ◽  
pp. 2250142
Author(s):  
Adel Alahmadi ◽  
Alaa Altassan ◽  
Widyan Basaffar ◽  
Hatoon Shoaib ◽  
Alexis Bonnecaze ◽  
...  
Keyword(s):  
Local Ring ◽  
Algebraic Structure ◽  
Invariant Theory ◽  
Linear Codes ◽  
Hamming Weight ◽  
Dual Codes ◽  
Weight Enumerators ◽  
Type Iv ◽  
Commutative Local Ring ◽  
Torsion Codes

There is a special local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by [Formula: see text] We study the algebraic structure of linear codes over that non-commutative local ring, in particular their residue and torsion codes. We introduce the notion of quasi self-dual codes over [Formula: see text] and Type IV codes, that is quasi self-dual codes whose all codewords have even Hamming weight. We study the weight enumerators of these codes by means of invariant theory, and classify them in short lengths.

scholarly journals On the complete weight enumerators of some reducible cyclic codes

2015 ◽  
Vol 338 (12) ◽  
pp. 2275-2287 ◽  
Author(s):  
Sunghan Bae ◽  
Chengju Li ◽  
Qin Yue
Keyword(s):  
Cyclic Codes ◽  
Weight Enumerators
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