On Isometric Error-Correcting Codes over Finite Fields of Prime Order

T. I. Katsaounis

Abstract


Error-correcting codes obtained from each other via a Hamming distance preserving transformation, called isometry, are equivalent. In this paper, we consider three different isometries which yield permutationally equivalent linear codes, monomially equivalent linear codes, and equivalent nonlinear codes, respectively. For each case, we derive some new necessary and sufficient conditions for equivalence using the concept of weight vector of a code or distance matrix of a code. Results hold for error-correcting codes over a finite field of prime order.

Keywords


Error-correcting code; Isometry; Permutational equivalence; Linear equivalence; Equivalent codes

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References


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DOI: http://dx.doi.org/10.26713%2Fjims.v10i1-2.677

eISSN 0975-5748; pISSN 0974-875X