On List Decoding of Mahdavifar-Vardy Codes

This paper addresses three problems concerning the list decoding algorithm for Mahdavifar--Vardy (MV) codes. First, the condition of decodability is derived assuming the presence of erasures over the operation channel. Second, we introduce multiplicity into the interpolation step of the algorithm, attempting to obtain a greater decoding radius. However, our results show that the decoding radius is sightly reduced when multiplicity is taken into account, due to properties of linearized polynomials. Finally, to evaluate the error performance of the list decoding algorithm of MV codes, we form a nearest neighbor decoder, and derive its decoder error probability.