Weight enumerators of self-dual codes

1991 ◽  
Vol 37 (4) ◽  
pp. 1222-1225 ◽  
Author(s):  
R.A. Brualdi ◽  
V.S. Pless
Keyword(s):  
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.

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 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 Complete weight enumerators of generalized doubly-even self-dual codes

2004 ◽  
Vol 10 (4) ◽  
pp. 540-550 ◽  
Author(s):  
Gabriele Nebe ◽  
H.-G. Quebbemann ◽  
E.M. Rains ◽  
N.J.A. Sloane
Keyword(s):  
Dual Codes ◽  
Weight Enumerators

scholarly journals On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116

10.37236/5213 ◽  
2015 ◽  
Vol 22 (4) ◽  
Author(s):  
Tao Zhang ◽  
Jerod Michel ◽  
Tao Feng ◽  
Gennian Ge
Keyword(s):  
Automorphism Group ◽  
Research Problem ◽  
Dual Codes ◽  
Weight Enumerators

The existence of optimal binary self-dual codes is a long-standing research problem. In this  paper, we present some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group $D_{2p}$, where $p$ is a prime. These results are applied to construct new self-dual codes with length $78$ or $116$. We obtain $16$ inequivalent self-dual $[78,39,14]$ codes, four of which have new weight enumerators. We also show that there are at least $141$ inequivalent self-dual $[116,58,18]$ codes, most of which are new up to equivalence. Meanwhile, we give some restrictions on the weight enumerators of singly even self-dual codes. We use these restrictions to exclude some possible weight enumerators of self-dual codes with lengths $74$, $76$, $82$, $98$ and $100$.

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