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While a recent construction by Calis and Koyluoglu generates $(r;s)$ PMDS codes for all $r$ and $s$, its field size is exponentially large.

Our proof technique's strength is based primarily on reducing inherent combinatorics in the proof.The problem of constructing convolutional codes with design generalized column distance remains an interesting open problem that requires further research.We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes.This paper considers the problem of designing maximum distance separable (MDS) codes over small fields with constraints on the support of their generator matrices.For any given $m\times n$ binary matrix $M$, the , states that if $M$ satisfies the so-called MDS condition, then for any field $\mathbb$ of size $q\geq n m-1$, there exists an $[n,m]_q$ MDS code whose generator matrix $G$, with entries in $\mathbb$, fits $M$ (i.e., $M$ is the support matrix of $G$).

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