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A matrix ring description for cyclic convolutional codes
Group convolutional codes
1. | Departamento de Matemática Aplicada, Universidad de Murcia. Campus de Espinardo, 30100 Espinardo, Murcia, Spain |
2. | Departamento de Álgebra y Análisis Matemático, Universidad de Almería, 04120 Almería, Spain, Spain, Spain |
[1] |
Gianira N. Alfarano, Anina Gruica, Julia Lieb, Joachim Rosenthal. Convolutional codes over finite chain rings, MDP codes and their characterization. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022028 |
[2] |
Somphong Jitman, San Ling, Patanee Udomkavanich. Skew constacyclic codes over finite chain rings. Advances in Mathematics of Communications, 2012, 6 (1) : 39-63. doi: 10.3934/amc.2012.6.39 |
[3] |
Delphine Boucher, Patrick Solé, Felix Ulmer. Skew constacyclic codes over Galois rings. Advances in Mathematics of Communications, 2008, 2 (3) : 273-292. doi: 10.3934/amc.2008.2.273 |
[4] |
Hai Q. Dinh, Hien D. T. Nguyen. On some classes of constacyclic codes over polynomial residue rings. Advances in Mathematics of Communications, 2012, 6 (2) : 175-191. doi: 10.3934/amc.2012.6.175 |
[5] |
Olof Heden, Martin Hessler. On linear equivalence and Phelps codes. Addendum. Advances in Mathematics of Communications, 2011, 5 (3) : 543-546. doi: 10.3934/amc.2011.5.543 |
[6] |
José Ignacio Iglesias Curto. Generalized AG convolutional codes. Advances in Mathematics of Communications, 2009, 3 (4) : 317-328. doi: 10.3934/amc.2009.3.317 |
[7] |
Heide Gluesing-Luerssen. On isometries for convolutional codes. Advances in Mathematics of Communications, 2009, 3 (2) : 179-203. doi: 10.3934/amc.2009.3.179 |
[8] |
Jérôme Ducoat, Frédérique Oggier. On skew polynomial codes and lattices from quotients of cyclic division algebras. Advances in Mathematics of Communications, 2016, 10 (1) : 79-94. doi: 10.3934/amc.2016.10.79 |
[9] |
Alexis Eduardo Almendras Valdebenito, Andrea Luigi Tironi. On the dual codes of skew constacyclic codes. Advances in Mathematics of Communications, 2018, 12 (4) : 659-679. doi: 10.3934/amc.2018039 |
[10] |
Nuh Aydin, Yasemin Cengellenmis, Abdullah Dertli, Steven T. Dougherty, Esengül Saltürk. Skew constacyclic codes over the local Frobenius non-chain rings of order 16. Advances in Mathematics of Communications, 2020, 14 (1) : 53-67. doi: 10.3934/amc.2020005 |
[11] |
Steven T. Dougherty, Joe Gildea, Adrian Korban, Abidin Kaya. Composite constructions of self-dual codes from group rings and new extremal self-dual binary codes of length 68. Advances in Mathematics of Communications, 2020, 14 (4) : 677-702. doi: 10.3934/amc.2020037 |
[12] |
Joe Gildea, Adrian Korban, Abidin Kaya, Bahattin Yildiz. Constructing self-dual codes from group rings and reverse circulant matrices. Advances in Mathematics of Communications, 2021, 15 (3) : 471-485. doi: 10.3934/amc.2020077 |
[13] |
Joe Gildea, Abidin Kaya, Adam Michael Roberts, Rhian Taylor, Alexander Tylyshchak. New self-dual codes from $ 2 \times 2 $ block circulant matrices, group rings and neighbours of neighbours. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021039 |
[14] |
Maria Bortos, Joe Gildea, Abidin Kaya, Adrian Korban, Alexander Tylyshchak. New self-dual codes of length 68 from a $ 2 \times 2 $ block matrix construction and group rings. Advances in Mathematics of Communications, 2022, 16 (2) : 269-284. doi: 10.3934/amc.2020111 |
[15] |
Nabil Bennenni, Kenza Guenda, Sihem Mesnager. DNA cyclic codes over rings. Advances in Mathematics of Communications, 2017, 11 (1) : 83-98. doi: 10.3934/amc.2017004 |
[16] |
Zihui Liu. Galois LCD codes over rings. Advances in Mathematics of Communications, 2022 doi: 10.3934/amc.2022002 |
[17] |
Ram Krishna Verma, Om Prakash, Ashutosh Singh, Habibul Islam. New quantum codes from skew constacyclic codes. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021028 |
[18] |
Ranya Djihad Boulanouar, Aicha Batoul, Delphine Boucher. An overview on skew constacyclic codes and their subclass of LCD codes. Advances in Mathematics of Communications, 2021, 15 (4) : 611-632. doi: 10.3934/amc.2020085 |
[19] |
Crnković Dean, Vedrana Mikulić Crnković, Bernardo G. Rodrigues. On self-orthogonal designs and codes related to Held's simple group. Advances in Mathematics of Communications, 2018, 12 (3) : 607-628. doi: 10.3934/amc.2018036 |
[20] |
Heide Gluesing-Luerssen, Fai-Lung Tsang. A matrix ring description for cyclic convolutional codes. Advances in Mathematics of Communications, 2008, 2 (1) : 55-81. doi: 10.3934/amc.2008.2.55 |
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