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29-05-2020 | Original Paper

# Double quadratic residue codes and self-dual double cyclic codes

Authors: Arezoo Soufi Karbaski, Taher Abualrub, Steven T. Dougherty

## Abstract

In this paper, we introduce double Quadratic Residue Codes (QRC) of length $$n=p+q$$ for prime numbers p and q in the ambient space $${{\mathbb {F}}} _{2}^{p}\times {{\mathbb {F}}}_{2}^{q}.$$ We give the structure of separable and non-separable double QRC over this alphabet and we show that interesting double QR codes in this space exist only in the case when $$p=q.$$ We give the main properties for these codes such as their idempotent generators and their duals. We relate these codes to codes over rings and show how they can be used to construct interesting lattices. As an applications of these codes, we provide examples of self-dual, formally self-dual and optimal double QRC. We also provide examples of best known quantum codes that are derived from double-QRC in this setting.
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Title
Double quadratic residue codes and self-dual double cyclic codes
Authors
Taher Abualrub
Steven T. Dougherty
Publication date
29-05-2020
Publisher
Springer Berlin Heidelberg
Published in
Applicable Algebra in Engineering, Communication and Computing / Issue 2/2022
Print ISSN: 0938-1279
Electronic ISSN: 1432-0622
DOI
https://doi.org/10.1007/s00200-020-00437-9

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