Weight Distributions of Hamming Codes

Abstract

We derive a recursive formula determining the weight distribution of the [n = (qm − 1)/(q − 1), n − m, 3] Hamming code H(m, q), when (m, q−1) = 1. Here q is a prime power. The proof is based on Moisio’s idea of using Pless power moment identity together with exponential sum techniques. 

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