Bounds on Spectra of Codes with Known Dual Distance

Authors:
Ilia Krasikov;Simon Litsyn
Affiliations:
School of Mathematical Sciences, Tel-Aviv University, Ramat-Aviv 69978 Israel, and Beit-Berl College, Kfar-Sava, Israel;Department of Electrical Engineering-Systems, Tel-Aviv University, Ramat-Aviv 69978 Israel
Venue:
Designs, Codes and Cryptography
Year:
1998

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Abstract

We estimate the interval where the distance distributionof a code of length n and of given dual distanceis upperbounded by the binomial distribution. The binomial upperbound is shown to be sharp in this range in the sense that forevery subinterval of size about √n ln n thereexists a spectrum component asymptotically achieving the binomialbound. For self-dual codes we give a better estimate for theinterval of binomiality.