Peterson–Gorenstein–Zierler algorithm for skew RS codes

Abstract

We design a non-commutative version of the Peterson–Gorenstein–Zierler decoding algorithm for a class of codes that we call skew RS codes. These codes are left ideals of a quotient of a skew polynomial ring, which endow them of a sort of non-commutative cyclic structure. Since we work over an arbitrary field, our techniques may be applied both to linear block codes and convolutional codes. In particular, our decoding algorithm applies for block codes beyond the classical cyclic case.

Keywords:

• Skew cyclic codes
• linear block codes
• convolutional codes
• skew polynomials

AMS Subject Classifications:

• 94B15
• 94B35
• 94B10
• 15A03

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ministerio de Ecomomía y Competitividad (MINECO) and Fondo Europero de Desarrollo Regional (FEDER) [grant number MTM2013-41992-P] and by Agencia Española de Investigación (AEI) and Fondo Europeo de Desarrollo Regional (FEDER) [grant number MTM2016-78364-P]