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Malaysian Journal of Science, Volume 34, Issue 2, 2015, pp. 222-226

Macwilliams equivalence theorem for the lee weight over ℤ4p+1

Barra A. * 1
Abstract :

For codes over fields, the MacWilliams equivalence theorem give us a complete characterization when two codes are equivalent. Considering the important role of the Lee weight in coding theory, one would like to have a similar results for codes over integer residue rings equipped with the Lee weight. We would like to prove that the linear isomorphisms between two codes in ℤnm that is preserving the Lee weight are exactly the maps of the form f(x1,x2,...,xm) = (u1xσ(1),u2xσ(2),...,umxσ(m)) where u1,...,um ∈ {-1,1} and σ ∈ Sn. The problem is still largely open. Wood proved the result for codes over ℤn where n is a power of 2 or 3. In this paper we prove the result for prime n of the form 4p+1 where p is prime. 

Keywords : Codes over rings,Extension theorem,Lee weight,MacWilliams equivalence
Subject Area : General

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