A systematic construction of self-dual codes

2003 ◽  
Vol 49 (11) ◽  
pp. 3005-3009 ◽  
Author(s):  
J. Carlach ◽  
A. Otmani
Keyword(s):  
Dual Codes ◽  
Systematic Construction ◽  
Construction Of Self

Construction of self-dual codes over ℤ 2 m $\mathbb {Z}_{2^{m}}$

2016 ◽  
Vol 8 (1) ◽  
pp. 83-101
Author(s):  
Anuradha Sharma ◽  
Amit K. Sharma
Keyword(s):  
Dual Codes ◽  
Construction Of Self

scholarly journals New self-dual codes from $ 2 \times 2 $ block circulant matrices, group rings and neighbours of neighbours

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Joe Gildea ◽  
Abidin Kaya ◽  
Adam Michael Roberts ◽  
Rhian Taylor ◽  
Alexander Tylyshchak
Keyword(s):  
Circulant Matrix ◽  
Circulant Matrices ◽  
Group Rings ◽  
Unique Combination ◽  
Dual Codes ◽  
Construction Of Self ◽  
New Construction

<p style='text-indent:20px;'>In this paper, we construct new self-dual codes from a construction that involves a unique combination; <inline-formula><tex-math id="M1">\begin{document}$ 2 \times 2 $\end{document}</tex-math></inline-formula> block circulant matrices, group rings and a reverse circulant matrix. There are certain conditions, specified in this paper, where this new construction yields self-dual codes. The theory is supported by the construction of self-dual codes over the rings <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{F}_2 $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{F}_2+u \mathbb{F}_2 $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{F}_4+u \mathbb{F}_4 $\end{document}</tex-math></inline-formula>. Using extensions and neighbours of codes, we construct <inline-formula><tex-math id="M5">\begin{document}$ 32 $\end{document}</tex-math></inline-formula> new self-dual codes of length <inline-formula><tex-math id="M6">\begin{document}$ 68 $\end{document}</tex-math></inline-formula>. We construct 48 new best known singly-even self-dual codes of length 96.</p>

scholarly journals The build-up construction of quasi self-dual codes over a non-unital ring

2021 ◽  
pp. 2250143
Author(s):  
Adel Alahmadi ◽  
Alaa Altassan ◽  
Hatoon Shoaib ◽  
Amani Alkathiry ◽  
Alexis Bonnecaze ◽  
...  
Keyword(s):  
Local Ring ◽  
Recursive Construction ◽  
Dual Codes ◽  
Generators And Relations ◽  
Unital Ring ◽  
Type Iv ◽  
Orthogonal Codes ◽  
Construction Of Self

There is a local ring [Formula: see text] of order [Formula: see text] without identity for the multiplication, defined by generators and relations as [Formula: see text] We study a recursive construction of self-orthogonal codes over [Formula: see text] We classify, up to permutation equivalence, self-orthogonal codes of length [Formula: see text] and size [Formula: see text] (called here quasi self-dual codes or QSD) up to the length [Formula: see text]. In particular, we classify Type IV codes (QSD codes with even weights) up to [Formula: see text].

scholarly journals Construction of self-dual codes in the Rosenbloom-Tsfasman metric

2017 ◽  
Author(s):  
Vira Hari Krisnawati ◽  
Anzi Lina Ukhtin Nisa
Keyword(s):  
Dual Codes ◽  
Construction Of Self

scholarly journals Double bordered constructions of self-dual codes from group rings over Frobenius rings

2020 ◽  
Vol 12 (4) ◽  
pp. 769-784
Author(s):  
Joe Gildea ◽  
Rhian Taylor ◽  
Abidin Kaya ◽  
A. Tylyshchak
Keyword(s):  
Group Rings ◽  
Dual Codes ◽  
Weight Enumerators ◽  
Frobenius Rings ◽  
Construction Of Self ◽  
New Construction ◽  
New Codes

AbstractIn this work, we describe a double bordered construction of self-dual codes from group rings. We show that this construction is effective for groups of order 2p where p is odd, over the rings $\mathbb {F}_{2}+u\mathbb {F}_{2}$ F 2 + u F 2 and $\mathbb {F}_{4}+u\mathbb {F}_{4}$ F 4 + u F 4 . We demonstrate the importance of this new construction by finding many new binary self-dual codes of lengths 64, 68 and 80; the new codes and their corresponding weight enumerators are listed in several tables.

scholarly journals CONSTRUCTION OF SELF-DUAL CODES OVER F2+ uF2

2012 ◽  
Vol 49 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Sung-Hyu Han ◽  
Hei-Sook Lee ◽  
Yoon-Jin Lee
Keyword(s):  
Dual Codes ◽  
Construction Of Self

Construction of Self-Dual Codes

2008 ◽  
Vol 54 (8) ◽  
pp. 3826-3831 ◽  
Author(s):  
Han-Ping Tsai ◽  
Pei-Yu Shih ◽  
Ren-Yih Wu ◽  
Wen-Ku Su ◽  
Chien-Hung Chen
Keyword(s):  
Dual Codes ◽  
Construction Of Self
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