2017/07/31 by Diego Napp, Napp, Diego, Raquel Pinto +3
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Error Correcting Code Techniques
paper · pdf · doi:10.48550/arxiv.1708.00336
Rosenthal et al. introduced and thoroughly studied the notion of Maximum Distance Profile (MDP) convolutional codes over (non-binary) finite fields refining the classical notion of optimum distance profile, see for instance [18, p.164]. These codes have the property that their column distances are maximal among all codes of the same rate and the same degree. In this paper we aim at studying this fundamental notion in the context of convolutional codes over a finite ring. We extensively use the notion of p-encoder to present upper-bounds on the column distances which allow to introduce the notion of MDP in the context of finite rings. A constructive method for (non necessarily free) MDP convolutional codes over Z p r is presented.