Self-Dual Codes over the Integers Modulo 4

@article{Conway1993SelfDualCO,
  title={Self-Dual Codes over the Integers Modulo 4},
  author={John H. Conway and N. J. A. Sloane},
  journal={J. Comb. Theory, Ser. A},
  year={1993},
  volume={62},
  pages={30-45}
}
Abstract Michael Klemm has recently studied the conditions satisfied by the complete weight enumerator of a self-dual code over Z 4 , the ring of integers modulo 4. In the present paper we deduce analogues theorems for the “symmetrized” weight enumerator (which ignores the difference between +1 and −1 coordinates) and the Hamming weight enumerator. We give a number of examples of self-dual codes, including codes which realize the basic weight enumerators occurring in all these theorems, and the… CONTINUE READING
BETA

Similar Papers

Tables and Topics from this paper.

Citations

Publications citing this paper.
SHOWING 1-10 OF 99 CITATIONS

Self-Dual Codes over Z 4 and Unimodular Lattices : A Survey

VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Quaternary Quadratic Residue Codes andUnimodular LatticesAlexis

Bonnecaze, Rekha A., CalderbankPatrick, Sol
  • 1997
VIEW 14 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

Type II codes over Z4

VIEW 16 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

On the Residue Codes of Extremal Type II Z4-Codes of Lengths 32 and 40

  • Discrete Mathematics
  • 2011
VIEW 7 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

A SURVEY ON QUATERNARY CODES AND THEIR BINARY IMAGES

VIEW 5 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Mass formula for self-dual codes over Zp2

VIEW 9 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

Type II Codes over

VIEW 14 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

Applied Algebra, Algebraic Algorithms and Error-Correcting Codes

  • Lecture Notes in Computer Science
  • 1999
VIEW 10 EXCERPTS
CITES METHODS & BACKGROUND
HIGHLY INFLUENCED

ON SOME LINEAR CODES OVER Z2S

VIEW 9 EXCERPTS
CITES BACKGROUND
HIGHLY INFLUENCED

FILTER CITATIONS BY YEAR

1992
2018

CITATION STATISTICS

  • 19 Highly Influenced Citations

References

Publications referenced by this paper.
SHOWING 1-10 OF 30 REFERENCES

‘Ueber die Identita

M. Klemm
  • . t von MacWilliams fu . . r die Gewichtsfunktion von Codes’’, Arch. Math., 49
  • 1987
VIEW 16 EXCERPTS
HIGHLY INFLUENTIAL

On the theory of design’

E. F. Assmus, Jr.
  • Surveys in Combinatorics,
  • 1989
VIEW 1 EXCERPT

‘Further results on designs carried by a code’

K. Grey
  • Ars Comb., 26 B
  • 1988
VIEW 1 EXCERPT

‘Sphere Packings

J. H. Conway, N.J.A. Sloane
  • Lattices and Groups’’, Springer-Verlag, NY
  • 1988
VIEW 2 EXCERPTS

Bounds for codes over the unit circle

  • IEEE Trans. Information Theory
  • 1986
VIEW 1 EXCERPT

Combinatorial Theory’

M. Hall, Jr.
  • 1986