Academic Journal
Self-dual and LCD double circulant codes over a class of non-local rings
| العنوان: | Self-dual and LCD double circulant codes over a class of non-local rings |
|---|---|
| المؤلفون: | Prakash, Om, Yadav, Shikha, Islam, Habibul, Solé, Patrick |
| المساهمون: | Indian Institute of Technology Patna (IITP), Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS) |
| المصدر: | ISSN: 0101-8205. |
| بيانات النشر: | HAL CCSD Springer Verlag |
| سنة النشر: | 2022 |
| المجموعة: | Aix-Marseille Université: HAL |
| مصطلحات موضوعية: | Double circulant code, LCD code, Self-dual code, Gray map, Quasi-cyclic code Mathematics Subject Classification (2000) 94B05, 94B15, 94B35, 94B60, [INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT] |
| الوصف: | International audience ; Let F q be a finite field of order q = p m where p is an odd prime. This paper presents the study of self-dual and LCD double circulant codes over a class of finite commutative non-chain rings R q = F q +uF q +u 2 F q +• • •+u q−1 F q where u q = u. Here, the whole contribution is two-folded. Firstly, we enumerate self-dual and LCD double circulant codes of length 2n over R q , where n is an odd integer. Then by considering a dual-preserving Gray map ϕ, we show that Gray images of such codes are asymptotically good. Secondly, we investigate the algebraic structure of 1-generator quasi-cyclic (QC) codes over R q for q = 3. In that context, we present their generator polynomials along with their minimal generating sets and minimum distance bounds. Here, it is proved that ϕ(C) is an sq-QC code of length nq over F q if C is an s-QC code of length n over R q . |
| نوع الوثيقة: | article in journal/newspaper |
| اللغة: | English |
| Relation: | hal-03697624; https://hal.science/hal-03697624; https://hal.science/hal-03697624/document; https://hal.science/hal-03697624/file/Self-dual%20and%20LCD%20double%20circulant%20codes.pdf |
| الاتاحة: | https://hal.science/hal-03697624 https://hal.science/hal-03697624/document https://hal.science/hal-03697624/file/Self-dual%20and%20LCD%20double%20circulant%20codes.pdf |
| Rights: | info:eu-repo/semantics/OpenAccess |
| رقم الانضمام: | edsbas.1391A8E3 |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |