More results on the weight enumerator of product codes

Authors:
L. M.G.M. Tolhuizen
Affiliations:
Philips Res. Lab., Eindhoven
Venue:
IEEE Transactions on Information Theory
Year:
2006

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Abstract

We consider the product code Cp of q-ary linear codes with minimum distances dc and dr. The words in Cp of weight less than drdc+max(dr┌(dc/g)┐,dc┌(dr/q)┐) are characterized, and their number is expressed in the number of low-weight words of the constituent codes. For binary product codes, we give an upper bound on the number of words in Cp of weightless than min(dr(dc+┌(dc/2)┐+1)), dc(dr+┌(dr/2)┐+1) that is met with equality if Cc and Cr are (extended) perfect codes.