On the Existence of Perfect Linear Codes Over $${{\mathbb{Z}}_{{2^{l}}}}$$ with Respect to Homogenous Metric

Abstract

In this paper, we obtain bounds for error correcting codes of some particular homogeneous weights over the ring of integers modulo \({2^l( {l\ge 3})}\). We also study these bounds to check for perfect linear codes and have shown the non-existence of one error correcting perfect codes with respect to the homogeneous weight.