# A Complete Classification of Doubly Even Self-dual Codes of Length 40

@article{Betsumiya2012ACC, title={A Complete Classification of Doubly Even Self-dual Codes of Length 40}, author={Koichi Betsumiya and Masaaki Harada and Akihiro Munemasa}, journal={ArXiv}, year={2012}, volume={abs/1104.3727} }

A complete classification of binary doubly even self-dual codes of length 40 is given. As a consequence, a classification of binary extremal self-dual codes of length 38 is also given.

## 31 Citations

### On the Classification of Binary Self-Dual Codes

- Computer ScienceArXiv
- 2011

An efficient algorithm for classification of binary self-dual codes is presented and a complete classification of the self- dual codes of length 38 is given.

### Classification of Binary Self-Dual Codes of Length 40

- Computer ScienceIEEE Transactions on Information Theory
- 2015

An efficient isomorph-free generation algorithm for classification of binary self-dual codes with the minimum distance d = 4 is presented and a complete classification of allbinary self- dual codes of length 40 is given.

### An Algorithm for Classification of Binary Self-Dual Codes

- Computer ScienceIEEE Transactions on Information Theory
- 2012

An efficient algorithm for classification of binary self-dual codes is presented and a complete classification of the self- dual codes of length 38 is given.

### Extremal Type II ℤ4-codes constructed from binary doubly even self-dual codes of length 40

- Computer ScienceDiscret. Math.
- 2017

### Extremal Binary and Ternary Codes of Length 60 with an Automorphism of Order 29 and a Generalization

- Computer Science, MathematicsMathematics
- 2022

In this paper, all extremal Type I and Type III codes of length 60 with an automorphism of order 29 are classified up to equivalence. In both cases, it has been proven that there are three…

### Some extremal self-dual codes and unimodular lattices in dimension 40

- Mathematics, Computer ScienceFinite Fields Their Appl.
- 2013

### SELF-DUAL CODES FROM SMALLER LENGTHS OF SELF-DUAL CODES AND RECURSIVE ALGORITHM

- Computer Science
- 2013

For the binary case, it was shown that recursive algorithm is actually same with another so-called building-up construction method, which is mentioned here.

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

- Computer ScienceElectron. J. Comb.
- 2015

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.

### Self‐Dual Codes and the Nonexistence of a Quasi‐Symmetric 2‐(37,9,8) Design with Intersection Numbers 1 and 3

- Mathematics
- 2017

We prove that a certain binary linear code associated with the incidence matrix of a quasi‐symmetric 2‐(37, 9, 8) design with intersection numbers 1 and 3 must be contained in an extremal doubly even…

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An efficient algorithm for classification of binary self-dual codes is presented and a complete classification of the self- dual codes of length 38 is given.

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