Shadow bounds for self-dual codes
- 1 January 1998
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 44 (1) , 134-139
- https://doi.org/10.1109/18.651000
Abstract
Conway and Sloane (1990) have previously given an upper bound on the minimum distance of a singly-even self-dual binary code, using the concept of the shadow of a self-dual code. We improve their bound, finding that the minimum distance of a self-dual binary code of length n is at most 4[n/24]+4, except when n mod 24=22, when the bound is 4[n/24]+6. We also show that a code of length a multiple of 24 meeting the bound cannot be singly-even. The same technique gives similar results for additive codes over GF(4) (relevant to quantum coding theory)Keywords
This publication has 5 references indexed in Scilit:
- The Shadow Theory of Modular and Unimodular LatticesJournal of Number Theory, 1998
- A bound for divisible codesIEEE Transactions on Information Theory, 1992
- A new upper bound for the minimum of an integral lattice of determinant 1Bulletin of the American Mathematical Society, 1990
- A new upper bound on the minimal distance of self-dual codesIEEE Transactions on Information Theory, 1990
- An upper bound for self-dual codesInformation and Control, 1973