Modular and p-adic cyclic codes
Designs, Codes and Cryptography
Error-Correction Coding for Digital Communications
Error-Correction Coding for Digital Communications
On minimality of convolutional ring encoders
IEEE Transactions on Information Theory
Cyclic codes and quadratic residue codes over Z4
IEEE Transactions on Information Theory
Convolutional codes over groups
IEEE Transactions on Information Theory - Part 1
An efficient algorithm for constructing minimal trellises for codes over finite abelian groups
IEEE Transactions on Information Theory - Part 1
On behaviors and convolutional codes
IEEE Transactions on Information Theory - Part 1
Quaternary Convolutional Codes From Linear Block Codes Over Galois Rings
IEEE Transactions on Information Theory
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We address the concept of "minimal polynomial encoder" for finite support linear convolutional codes over ${\mathbb Z}_{p^r}$. These codes can be interpreted as polynomial modules which enables us to apply results from the 2007-paper [8] to introduce the notions of "p-encoder" and "minimal p-encoder". Here the latter notion is the ring analogon of a row reduced polynomial encoder from the field case. We show how to construct a minimal trellis representation of a delay-free finite support convolutional code from a minimal p-encoder. We express its number of trellis states in terms of a degree invariant of the code. The latter expression generalizes the wellknown expression in terms of the degree of a delay-free finite support convolutional code over a field to the ring case. The results are also applicable to block trellis realization of polynomial block codes over ${\mathbb Z}_{p^r}$, such as CRC codes over ${\mathbb Z}_{p^r}$.