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A note on constant weight cyclic codes

Harry T. Hsu, John E. Olson

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Abstract

In this paper we show that the dual code of a g-ary Hamming single error-correcting code is a constant weight cyclic code with weight q(m-1). We give, as a consequence, a very simple alternative derivation of the weight enumerator formula for the q-ary Hamming single error-correcting code. We show also that a binary cyclic equidistant code can be derived from this dual code

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What this paper is about

In this paper we show that the dual code of a g-ary Hamming single error-correcting code is a constant weight cyclic code with weight q(m-1). We give, as a consequence, a very simple alternative derivation of the weight enumerator formula for the q-ary Hamming single error-correcting code. We show also that a binary cyclic equidistant code can be derived from this dual code

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Available abstract

In this paper we show that the dual code of a g-ary Hamming single error-correcting code is a constant weight cyclic code with weight q(m-1). We give, as a consequence, a very simple alternative derivation of the weight enumerator formula for the q-ary Hamming single error-correcting code. We show also that a binary cyclic equidistant code can be derived from this dual code

Key concepts: Cyclic code, Constant-weight code, Hamming code, Hamming bound, Constant (computer programming), Code (set theory), Mathematics, Polynomial code

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