# On the Enumeration of Self-Dual Codes

@article{Conway1980OnTE,
title={On the Enumeration of Self-Dual Codes},
author={John H. Conway and Vera Pless},
journal={J. Comb. Theory, Ser. A},
year={1980},
volume={28},
pages={26-53}
}
• Published 1980
• Computer Science
• J. Comb. Theory, Ser. A
180 Citations
Self-Dual Codes over the Integers Modulo 4
• Computer Science, Mathematics
J. Comb. Theory, Ser. A
• 1993
A systematic construction of self-dual codes
• Computer Science
IEEE Trans. Inf. Theory
• 2003
A new coding construction scheme of block codes using short base codes and permutations that enables the construction of binary self-dual codes is presented and a new unified construction of the five extremal doubly-even self- dual codes is given.
Cyclic Self-Dual Codes1
There do not exist doubly-even cyclic self-dual codes, i.e. codes in which all weights are divisible by 4, as a consequence of Theorem 1.
An Enumeration of Binary Self-Dual Codes of Length 32
• Computer Science
Des. Codes Cryptogr.
• 2002
This paper has developed algorithms that will take lists of inequivalent small codes and produce lists of larger codes where each inequivalent code occurs only a few times and finds the size of the automorphism group so that the number of distinct binary self-dual codes for a specific length is found.
Type II Codes over
• Computer Science, Mathematics
• 2002
Type II 4-codes are introduced as self-dual codes over the integers modulo4 containing the all-one vector and with Euclidean weights multiple of 8. Their weight enumerators are characterized by means
Cyclic self-dual codes
• Computer Science
IEEE Trans. Inf. Theory
• 1983
It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4, and the shortest nontrivial code in this class is shown to have length 14.
Automorphisms of codes with applications to extremal doubly even codes of length 48
• W. C. Huffman
• Computer Science, Mathematics
IEEE Trans. Inf. Theory
• 1982
The main theorem proved is that an extremal self-dual doubly even code of length 48 with a nontrivial automorphism of odd order is equivalent to the extended quadratic residue code.
Self-dual codes over the Kleinian four group
Self-dual codes over the Kleinian four group K=Z2×Z2 for a natural quadratic form on Kn are introduced and the theory is developed.

## References

SHOWING 1-8 OF 8 REFERENCES
On the Classification and Enumeration of Self-Dual Codes
• Computer Science
J. Comb. Theory, Ser. A
• 1975
Self-Dual Codes over GF(4)
• Computer Science
J. Comb. Theory, Ser. A
• 1978
Self-Dual Codes over ${\text{GF}}( 3 )$
• Computer Science, Mathematics
• 1976
A number of Gleason-type theorems are given, describing the weight enumerators of self-dual and maximal self-orthogonal codes over GF, and the complete weight enumerator of various quadratic residue and symmetry codes of length $\leqq 60$ are obtained.
Good self dual codes exist
• Computer Science
Discret. Math.
• 1972