On the duality and the direction of polycyclic codes

Adel  Alahmadi; Steven  Dougherty; André  Leroy; Patrick  Solé

doi:10.3934/amc.2016049

Article Contents

2016, Volume 10, Issue 4: 921-929. Doi: 10.3934/amc.2016049

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On the duality and the direction of polycyclic codes

1.
Math Dept., King Abdulaziz University, Jeddah
2.
University of Scranton, Scranton, PA 18518
3.
University of Artois, Faculté J. Perrin, 62300 Lens
4.
CNRS/LAGA, University of Paris 8, 93 526 Saint-Denis

Received: February 28, 2015

Published: October 2016

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Abstract

Polycyclic codes are ideals in quotients of polynomial rings by a principal ideal. Special cases are cyclic and constacyclic codes. A MacWilliams relation between such a code and its annihilator ideal is derived. An infinite family of binary self-dual codes that are also formally self-dual in the classical sense is exhibited. We show that right polycyclic codes are left polycyclic codes with different (explicit) associate vectors and characterize the case when a code is both left and right polycyclic for the same associate polynomial. A similar study is led for sequential codes.

Keywords:

Cyclic codes,
formally self-dual codes.

Mathematics Subject Classification: Primary: 94B15, 94B05, 94B065.

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