Self-dual codes over GF(3) and GF(4) of length not exceeding 16

@article{Conway1979SelfdualCO,
  title={Self-dual codes over GF(3) and GF(4) of length not exceeding 16},
  author={John H. Conway and Vera Pless and N. J. A. Sloane},
  journal={IEEE Trans. Inf. Theory},
  year={1979},
  volume={25},
  pages={312-322}
}
All self-dual codes over GF(3) and GF(4) of length 16 are found. The self-dual codes of shorter length are described in a concise and systematic notation. A number of new techniques ("promotion" and "demotion," "tag olng? and "subtraction") are given for constructing codes. Finally, several new extremal self-dual codes are given which have length greater than 16. 
Self-Dual Codes over GF(5)
New self-dual codes over GF(4) with the highest known minimum weights
  • Jon-Lark Kim
  • Computer Science, Mathematics
    IEEE Trans. Inf. Theory
  • 2001
The purpose of this correspondence is to construct new Hermitian self-dual codes over GF(4) of lengths 22, 24, 26, 32, and 34 which have the highest known minimum weights. In particular, for length
New good Hermitian self-dual codes over GF(4)
  • Jon-Lark Kim
  • Computer Science
    Proceedings. 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252)
  • 2001
TLDR
This paper constructs 8 new extremal self-dual [22,11,8] codes over GF(4) which do not have a nontrivial automorphism of odd order.
Self-dual Codes-Theme and Variations
Self-dual codes over GF(2), GF(3) and GF(4) were classified from the early 70's until the early 80's. A method for how to do this and efficient descriptions of the codes were developed [3, 4, 17, 20,
Self-dual codes over GF(7)
TLDR
A generator matrix, Hamming weight distribution, and order of the monomial group of each of the self-orthogonal and self-dual codes of length n are given.
On ternary self-dual codes of length 24
TLDR
A partial classification is given of the self-dual codes of length 24 over GF (3) and it is found that there are exactly two codes with minimum Hamming distance d=9 and most of the codes have d=6 and are indecomposable.
A SOME PROPERTIES OF LINEAR CODES OVER GF (4)
TLDR
The aim of this note is to highlight certain properties of linear codes over GF (4) and even formally self codes.
Weight Enumerators of Self-Orthogonal Codes over $GF$(3)
The Hamming and complete weight enumerators of maximally self-orthogonal codes over $GF$(3) of lengths $12m - 1$, $12m$ and $12m + 1$ are characterized. The results for length $12m + 1$ are believed
New constructions of optimal self-dual binary codes of length 54
TLDR
The quaternary Hermitian self-dual [18,9,6]4 codes are classified and used to construct new binary self- dual [54,27,10]2 codes, which have automorphisms of order 3 and six of their weight enumerators have not been previously encountered.
On cyclic reversible self-dual additive codes with odd length over Z22
TLDR
All cyclic and reversible [5,2.5,3] additive codes over Z/sub 2//sup 2/ are isomorphic and possess interesting properties.
...
...

References

SHOWING 1-10 OF 19 REFERENCES
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.
Self-Dual Codes over GF(4)
On the Enumeration of Self-Dual Codes
On the Classification and Enumeration of Self-Dual Codes
The children of the (32, 16) doubly even codes
  • V. Pless
  • Computer Science
    IEEE Trans. Inf. Theory
  • 1978
Generator matrices, weight distributions, and automorphism groups are given for all (26,13,6), (28,14,6), and (30,15,6) binary self-dual codes. These results are obtained from the earlier enumeration
Symmetry Codes over GF(3) and New Five-Designs
  • V. Pless
  • Computer Science
    J. Comb. Theory, Ser. A
  • 1972
Codes over GF ( 4 ) and Complex Lattices
The connections between binary and ternary error-correcting codes on the one hand, and lattices and sphere-packings in W on the other have been studied by several authors [6,7,
...
...