Singly Even Self-Dual Codes With Minimal Shadow

@article{Bouyuklieva2012SinglyES,
  title={Singly Even Self-Dual Codes With Minimal Shadow},
  author={Stefka Bouyuklieva and Wolfgang Willems},
  journal={IEEE Transactions on Information Theory},
  year={2012},
  volume={58},
  pages={3856-3860}
}
In this paper, extremal singly even self-dual codes with minimal shadow are investigated. Nonexistence of such codes for particular parameters is proved. By a result of Rains, the length of extremal singly even self-dual codes is bounded. Explicit bounds are given in case the shadow is minimal. 
View on IEEE
arxiv.org
8 Citations
Highly Influential Citations
1
Background Citations
5

Tables from this paper

8 Citations

Additive Self-Dual Codes over GF(4) with Minimal Shadow
TLDR
It is proved the nonexistence of extremal Type I additive self-dual codes over G F with minimal shadow for some parameters.
Neighborhoods of binary self-dual codes
TLDR
It is shown that for codelength divisible by 8 such a neighborhood consists of three self-dual codes, two are doubly- even and one is always singly-even.
New MDS self-dual codes over finite fields of odd characteristic
TLDR
New classes of MDS self-dual codes via (extended) generalized Reed–Solomon codes over finite fields of odd characteristic are produced.
Singly even self-dual codes of length 24k + 10 and minimum weight 4k + 2
  • M. Harada
  • Computer Science
    Cryptography and Communications
  • 2018
TLDR
Some restrictions on the possible weight enumerators of singly even self-dual [24k + 10, 12k + 5, 4k + 2] codes with shadows of minimum weight at least 5 for k = 2, 3, 4, 5 are given.
Near-Extremal Type I Self-Dual Codes with Minimal Shadow over GF(2) and GF(4)
Binary self-dual codes and additive self-dual codes over GF(4) contain common points. Both have Type I codes and Type II codes, as well as shadow codes. In this paper, we provide a comprehensive…
The search of Type I codes
TLDR
The purpose of this paper is to investigate interesting properties of Type I codes of different lengths, and to build up a computer-based code-searching program based on knowledge about Type I code.
Extremal self-dual codes
TLDR
The best singly- even codes are determined and it is proved that these always perform better than doubly-even codes with the same parameters, and a new easy-to-handle criterion is provided to determine possible cycle structures of the automorphisms of binary extremal codes.
On the Existence of Certain Optimal Self-Dual Codes with Lengths Between 74 and 116
TLDR
This paper presents some results concerning the decomposition of binary self-dual codes with a dihedral automorphism group D_{2p}$, where p is a prime, and gives some restrictions on the weight enumerators of singly even self- dual codes.

References

SHOWING 1-10 OF 23 REFERENCES
Weight enumerators of self-dual codes
Some construction techniques are investigated for self-dual codes, and construct a singly-even self-dual (48,24,10kode with a weight enumerator that was not known to be attainable.
Shadow Bounds for Self-Dual Codes
  • E. Rains
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1998
TLDR
It is shown that a code of length a multiple of 24 meeting the bound cannot be singly-even, and the same technique gives similar results for additive codes over GF(4) (relevant to quantum coding theory).
On the minimal weight of some singly-even codes
  • V. Yorgov
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1999
It is shown that the minimal distance d of a singly-even self-dual [24t+8, 12t+4] code is at most 4t+2 if its shadow contains a weight 4 vector, t is even, and (/sub t//sup 5t/) is odd. It is proved…
Some connections between self-dual codes, combinatorial designs and secret sharing schemes
TLDR
This work studies a class of singly-even self-dual codes with the special property that the minimum weight of their shadow is 1 and describes two types of schemes based on codes, the first is an one-part secret sharing scheme and the second is a two-part sharing scheme.
The Existence of a Self-Dual 70, 35, 12] Code and Formally Self-Dual Codes
TLDR
A construction for self-dual codes is presented, based on extending generator matrices, which results in the first published example of a singly-even 70, 35, 12] code.
NONEXISTENCE OF SOME EXTREMAL SELF-DUAL CODES
TLDR
This work calculates m's which correspond to the nonexistence of some extremal self-dual binary linear codes and proves that there are inflnitely many such m's.
New asymptotic bounds for self-dual codes and lattices
  • E. Rains
  • Computer Science
    IEEE Trans. Inf. Theory
  • 2003
We give an independent proof of the Krasikov-Litsyn bound d/n/spl lsim/(1-5/sup -1/4/)/2 on doubly-even self-dual binary codes. The technique used (a refinement of the Mallows-Odlyzko-Sloane…
On the Classification and Enumeration of Self-Dual Codes
Extremal self-dual codes of lengths 66 and 68
TLDR
New extremal self-dual codes of dimensions 33 and 34 are obtained and these codes are applied to the determinants of EMT and EMT in the framework of discrete-time EMT.
On the Classification of Extremal $[36,18,8]$ Binary Self-Dual Codes
TLDR
A new recursive method to classify extremal self-dual codes is given and all the 41 extremal binary [36,18,8] self- dual codes are classified.
...
...