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}
}
The Binary Self-Dual Codes of Length up to 32: A Revised Enumeration
Self-Dual Codes over the Integers Modulo 4
A systematic construction of self-dual codes
TLDR
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
TLDR
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
TLDR
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
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
TLDR
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.
On the classification and enumeration of self-dual codes
Automorphisms of codes with applications to extremal doubly even codes of length 48
  • W. C. Huffman
  • Computer Science, Mathematics
    IEEE Trans. Inf. Theory
  • 1982
TLDR
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
TLDR
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.
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References

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On the Classification and Enumeration of Self-Dual Codes
Self-Dual Codes over GF(4)
Self-Dual Codes over ${\text{GF}}( 3 )$
TLDR
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.