Classification of perfect linear codes with crown poset structure

Abstract

Brualdi et al. introduced the concept of poset codes. In this paper, we consider the problem of classifying all perfect linear codes when the set of coordinate positions is endowed with crown poset structure. We derive a Ramanujan-Nagell type diophantine equation which is satisfied by parameters of perfect linear P-code. Solving this equation, we characterize parameters of one and two error correcting perfect linear P-codes. (C) 2002 Elsevier Science B.V. All rights reserved.