• Corpus ID: 239016757

The search of Type I codes

@article{Hannusch2021TheSO,
  title={The search of Type I codes},
  author={Carolin Hannusch and S. Roland Major},
  journal={ArXiv},
  year={2021},
  volume={abs/2110.09244}
}
A self-dual binary linear code is called Type I code if it has singly-even codewords, i.e. it has codewords with weight divisible by 2. The purpose of this paper is to investigate interesting properties of Type I codes of different lengths. Further, we build up a computer-based code-searching program based on our knowledge about Type I codes. Some computation results achieved by this program are given. 

Tables from this paper

References

SHOWING 1-9 OF 9 REFERENCES
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).
New Binary Singly Even Self-Dual Codes
TLDR
In this paper, new binary singly even self-dual codes with larger minimum weights than the previously known singlyEven self- dual codes are constructed for several lengths.
Weight enumerators of self-dual codes
TLDR
It is shown that there exists a singly-even self-dual code C' of length n=48 and minimum weight d=10 whose weight enumerator is prescribed in the work of J.H. Conway et al.
Singly Even Self-Dual Codes With Minimal Shadow
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
Selected Unsolved Problems in Coding Theory
TLDR
Codes and Lattices, Kittens and Blackjack, RH and Coding Theory, Hyperelliptic Curves and QR Codes, and Codes from Modular Curves are reviewed.
Nonexistence of Certain Singly Even Self-Dual Codes with Minimal Shadow
TLDR
It is demonstrated that the weight enumerator of a singly even self-dual code with minimal shadow is not uniquely determined for parameters $[24m+6, 12m+3,4m+2]$ and $[ 24m+22,12m+11, 4m+4]$.
Introduction to Coding Theory Lecture Notes
These are lecture notes for an advanced undergraduate (and beginning graduate) course in Coding Theory in the Computer Science Department at Bar-Ilan University. These notes contain the technical
Open problems in coding theory
  • In: Contemp. Math
  • 2015
Brualdi and VS Pless . “ Weight enumerators of self - dual codes ”
  • 1991