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Self-Dual Codes over Rk and Binary Self-Dual Codes

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2013

Key Words:

Author NameUniversity of Author

AMS Codes:

Abstract (2. Language): 
We study self-dual codes over an infinite family of rings, denoted Rk, which has been recently introduced to the literature. We prove that for each self-dual code over Rk, k ≥ 2, there exist a corresponding binary self-dual code, a real unimodular lattice, a complex unimodular lattice, a quaternionic lattice and an infinite family of self-dual codes. We prove the existence of Type II codes of all lengths over Rk, for k ≥ 3, and we obtain some extremal binary self-dual codes including the extended binary Golay code as the Gray images of self-dual codes over Rk for some suitable k. The binary self-dual codes obtained from Rk all have automorphism groups whose orders are a multiple of 2k.
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  • 1
89-106
  • English

REFERENCES

References: 

[1] E. Bannai, S.T. Dougherty, M. Harada, and M. Oura. Type II Codes, Even Unimodular
Lattices, and Invariant Rings, IEEE Transactions on Information Theory, 45:1194-1205,
1999.
[2] Y.J. Choie and S.T. Dougherty. Codes over 2m and Jacobi Forms over the Quaternions,
Applicable Algebra in Engineering, Communications and Computing 15:129-147, 2004.
[3] J.H. Conway and N.J.A. Sloane. Sphere Packing, Lattices and Groups (2nd ed.), New
York: Springer-Verlag, 1993.
[4] J. H. Conway and N. J. A. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag,
NY, 3rd ed., 1998.
[5] S.T. Dougherty, T. A. Gulliver and M. Harada. Type II self-dual codes over finite rings
and even unimodular lattices, Journal of Algebraic Combinatorics, 9:233–250, 1999.
REFERENCES 106
[6] S.T. Dougherty, M. Harada, P. Gaborit, and P. Solé. Type II Codes Over F2 + uF2, IEEE
Transactions on Information Theory, 45:32-45, 1999.
[7] S.T. Dougherty, B. Yıldız and S. Karadeniz. Codes over Rk, Gray Maps and their Binary
Images, Finite Fields and their Applications 17:205–219, 2011.
[8] F.J. MacWilliams and N.J.A. Sloane. The Theory of Error-Correcting Codes. Amsterdam:
North-Holland, 1977.
[9] G. Nebe, E.M. Rains and N. J. A. Sloane. Self-Dual Codes and Invariant Theory. Springer-
Verlag, 2006.
[10] E.M. Rains. Shadow Bounds for self-dual Codes, IEEE Transactions on Information Theory,
44:134–139, 1998.
[11] J. Wood. Duality for modules over finite rings and applications to coding theory. American
Journal of Mathematics, 121:555-575, 1999.

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