Construction of linear codes over Σ=P4s=0 vs5A4

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dc.citation.epage158
dc.citation.issue1
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage147
dc.contributor.affiliationУніверситет Мостефи Бен Булейд
dc.contributor.affiliationMostefa Ben Boulaid University
dc.contributor.authorМалкі, М.
dc.contributor.authorШату, К.
dc.contributor.authorMalki, M.
dc.contributor.authorChatouh, K.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T11:54:49Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractМета цієї статті — запропонувати нове сімейство кодів. Ми визначаємо цю сім’ю над кільцем Σ=P4s=0 vs5A4, з v55 = v5. Виводимо його властивості, матрицю-генератор і зображення Грея. Це нове сімейство кодів проілюстровано за допомогою трьох програм.
dc.description.abstractThe aim of this paper is to propose a new family of codes. We define this family over the ring Σ=P4s=0 vs5A4, with v55 = v5. We derive its properties, a generator matrix and Gray images. This new family of codes is illustrated by three applications.
dc.format.extent147-158
dc.format.pages12
dc.identifier.citationMalki M. Construction of linear codes over Σ=P4s=0 vs5A4 / M. Malki, K. Chatouh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 147–158.
dc.identifier.citationenMalki M. Construction of linear codes over Σ=P4s=0 vs5A4 / M. Malki, K. Chatouh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 1. — P. 147–158.
dc.identifier.doi10.23939/mmc2023.01.147
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63486
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 1 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 1 (10), 2023
dc.relation.references[1] Chatouh K., Guenda K., Aaron Gulliver T. New classes of codes over Rq,p,m = Zpm[u1, u2, · · · , uq]/hu2 i = 0, uiuj − ujuii and their applications. Computational and Applied Mathematics. 39, 152 (2020).
dc.relation.references[2] Yildiz B., Karadeniz S. Linear codes over Z4 +uZ4: MacWilliams identities, projections, formally self-dual codes. Finite Fields and Their Applications. 27, 24–40 (2014).
dc.relation.references[3] Klemm M. Selbstduale Codes ¨uber dem Ring der ganzen Zahlen modulo 4. Archiv der Mathematik. 53 (2), 201–207 (1989).
dc.relation.references[4] Hammons A. R., Kumar P. V., Calderbank A. R., Sloane N. J. A., Sol´e P. The Z4-linearity of Kerdock, Preparata, Goethals and related codes. IEEE Transactions on Information Theory. 40 (2), 301–319 (1994).
dc.relation.references[5] Hammons A. R., Kumar P. V., Calderbank A. R., Sloane N. J. A., Sol´e P. On the apparent duality of the Kerdock and Preparata codes. International Symposium on Applied Algebra, Algebraic Algorithms and Error–Correcting Codes. 13–24 (1993).
dc.relation.references[6] Bustomi, Santika A. P., Suprijanto D. Linear codes over the ring Z4 + uZ4 + vZ4 + wZ4 + uvZ4 + uwZ4 + vwZ4 + uvwZ4. Preprint arXiv:1904.11117v1 (2019).
dc.relation.references[7] Li P., Guo X., Zhu S., Kai X. Some results on linear codes over the ring Z4 + uZ4 + vZ4 + uvZ4. Journal of Applied Mathematics and Computing. 54 (1–2), 307-324 (2017).
dc.relation.references[8] Ndiaye O. One cyclic codes over Fpk + vFpk + v2Fpk +...+ vrFpk . Gulf Journal of Mathematics. 4 (4),(2016).
dc.relation.references[9] Liu Y., Shi M., Sol´e P. Quadratic Residue Codes over Fp + vFp + v 2Fp. International Workshop on the Arithmetic of Finite Fields. 204–211 (2014).
dc.relation.references[10] Qian J.-F., Zhang L.-N., Zhu S.-X. Cyclic Codes over Fp + uFp +...+ uk−1Fp. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E88-A (3), 795–797 (2005).
dc.relation.references[11] Aydin N., Ray-Chaudhuri D. K. Quasi-cyclic codes over Z4 and some new binary codes. IEEE Transactions on Information Theory. 48 (7), 2065–2069 (2002).
dc.relation.references[12] Gao J., Shi M., Wu T., Fu F.-W. On double cyclic codes over Z4. Finite Fields and Their Applications. 39, 233–250 (2016).
dc.relation.references[13] Melakhessou A., Guenda K., Gulliver T. A., Shi M., Sol´e P. On Codes over Fq + vFq + v 2Fq. Journal of Applied Mathematics and Computing. 57 (1), 375–391 (2018).
dc.relation.references[14] Grassl M. Bounds on the minimum distance of linear codes and quantum codes. Online available at www.codetables.de. Accessed on 2021/08/20 (2019).
dc.relation.referencesen[1] Chatouh K., Guenda K., Aaron Gulliver T. New classes of codes over Rq,p,m = Zpm[u1, u2, · · · , uq]/hu2 i = 0, uiuj − ujuii and their applications. Computational and Applied Mathematics. 39, 152 (2020).
dc.relation.referencesen[2] Yildiz B., Karadeniz S. Linear codes over Z4 +uZ4: MacWilliams identities, projections, formally self-dual codes. Finite Fields and Their Applications. 27, 24–40 (2014).
dc.relation.referencesen[3] Klemm M. Selbstduale Codes ¨uber dem Ring der ganzen Zahlen modulo 4. Archiv der Mathematik. 53 (2), 201–207 (1989).
dc.relation.referencesen[4] Hammons A. R., Kumar P. V., Calderbank A. R., Sloane N. J. A., Sol´e P. The Z4-linearity of Kerdock, Preparata, Goethals and related codes. IEEE Transactions on Information Theory. 40 (2), 301–319 (1994).
dc.relation.referencesen[5] Hammons A. R., Kumar P. V., Calderbank A. R., Sloane N. J. A., Sol´e P. On the apparent duality of the Kerdock and Preparata codes. International Symposium on Applied Algebra, Algebraic Algorithms and Error–Correcting Codes. 13–24 (1993).
dc.relation.referencesen[6] Bustomi, Santika A. P., Suprijanto D. Linear codes over the ring Z4 + uZ4 + vZ4 + wZ4 + uvZ4 + uwZ4 + vwZ4 + uvwZ4. Preprint arXiv:1904.11117v1 (2019).
dc.relation.referencesen[7] Li P., Guo X., Zhu S., Kai X. Some results on linear codes over the ring Z4 + uZ4 + vZ4 + uvZ4. Journal of Applied Mathematics and Computing. 54 (1–2), 307-324 (2017).
dc.relation.referencesen[8] Ndiaye O. One cyclic codes over Fpk + vFpk + v2Fpk +...+ vrFpk . Gulf Journal of Mathematics. 4 (4),(2016).
dc.relation.referencesen[9] Liu Y., Shi M., Sol´e P. Quadratic Residue Codes over Fp + vFp + v 2Fp. International Workshop on the Arithmetic of Finite Fields. 204–211 (2014).
dc.relation.referencesen[10] Qian J.-F., Zhang L.-N., Zhu S.-X. Cyclic Codes over Fp + uFp +...+ uk−1Fp. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. E88-A (3), 795–797 (2005).
dc.relation.referencesen[11] Aydin N., Ray-Chaudhuri D. K. Quasi-cyclic codes over Z4 and some new binary codes. IEEE Transactions on Information Theory. 48 (7), 2065–2069 (2002).
dc.relation.referencesen[12] Gao J., Shi M., Wu T., Fu F.-W. On double cyclic codes over Z4. Finite Fields and Their Applications. 39, 233–250 (2016).
dc.relation.referencesen[13] Melakhessou A., Guenda K., Gulliver T. A., Shi M., Sol´e P. On Codes over Fq + vFq + v 2Fq. Journal of Applied Mathematics and Computing. 57 (1), 375–391 (2018).
dc.relation.referencesen[14] Grassl M. Bounds on the minimum distance of linear codes and quantum codes. Online available at www.codetables.de. Accessed on 2021/08/20 (2019).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectкоди над кільцями
dc.subjectідемпотенти
dc.subjectвідображення Грея
dc.subjectcodes over the rings
dc.subjectidempotents
dc.subjectGray map
dc.titleConstruction of linear codes over Σ=P4s=0 vs5A4
dc.title.alternativeПобудова лінійних кодів над Σ=P4s=0 vs5A4
dc.typeArticle

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Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 1