Application of Constacyclic Codes Over the Semi Local Ring $${F_{{p^m}}} + v{F_{{p^m}}}$$

Tushar Bag (), Abdullah Dertli (), Yasemin Cengellenmis () and Ashish K. Upadhyay ()
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Tushar Bag: Indian Institute of Technology Patna
Abdullah Dertli: Ondokuz Mayis University, Faculty of Arts and Sciences
Yasemin Cengellenmis: Trakya University, Faculty of Sciences
Ashish K. Upadhyay: Indian Institute of Technology Patna

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 1, 265-275

Abstract: Abstract In this paper, we study the quantum codes over $${F_{{p^m}}}$$, which are obtained from (λ1 + λ2)-constacyclic codes over the semi local ring $${F_{{p^m}}} + v{F_{{p^m}}}$$, where v2 = 1, p is odd prime. We decompose a (λ1 + λ2)-constacyclic code over $${F_{{p^m}}} + v{F_{{p^m}}}$$ into two constacyclic codes over $${F_{{p^m}}}$$ such as (λ1 + λ2)-constacyclic and (λ1–λ2)-constacyclic. We give the necessary and sufficient condition that the (λ1 + vλ2)-constacyclic codes over $${F_{{p^m}}} + v{F_{{p^m}}}$$ contain their duals. We give some examples of non binary quantum codes.

Keywords: Gray map; cyclic code; negacyclic code; constacyclic codes; quantum codes; 94B05; 94B15; 94B60 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0399-3

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