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On extendability of additive code isometries
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An approach to the performance of SPC product codes on the erasure channel
Convolutional codes with a matrix-algebra word-ambient
1. | Department of Algebra and CITIC-UGR, University of Granada, E18071 Granada |
2. | Department of Computer Sciences and AI, and CITIC, Universidad de Granada, E51001 Ceuta, Spain |
References:
[1] |
S. Estrada, J. R. García-Rozas, J. Peralta and E. Sánchez-García, Group convolutional codes, Adv. Math. Commun., 2 (2008), 83-94.
doi: 10.3934/amc.2008.2.83. |
[2] |
G. D. Forney Jr., Convolutional codes I: Algebraic structure, IEEE Trans. Inf. Theory, 16 (1970), 720-738,
doi: 10.1109/TIT.1970.1054541. |
[3] |
H. Gluesing-Luerssen and W. Schmale, On cyclic convolutional codes, Acta Appl. Math., 82 (2004), 183-237.
doi: 10.1023/B:ACAP.0000027534.61242.09. |
[4] |
J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Ideal codes over separable ring extensions, preprint, arXiv:1408.1546 |
[5] |
J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Cyclic convolutional codes over separable extensions, in Coding Theory and Applications (eds. R. Pinto, P. Rocha Malonek and P. Vettori), Springer, 2015, 209-215.
doi: 10.1007/978-3-319-17296-5_22. |
[6] |
K. Hirata and K. Sugano, On semisimple extensions and separable extensions over non commutative rings, J. Math. Soc. Japan, 18 (1966), 360-373.
doi: 10.2969/jmsj/01840360. |
[7] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, 1994.
doi: 10.1017/CBO9780511840371. |
[8] |
N. Jacobson, Basic Algebra: II, W. H. Freeman Company, 1980. |
[9] |
S. R. López-Permouth and S. Szabo, Convolutional codes with additional algebraic structure, J. Pure Appl. Algebra, 217 (2013), 958-972.
doi: 10.1016/j.jpaa.2012.09.017. |
[10] |
R. Pierce, Associative Algebras, Springer-Verlag, 1982,
doi: 10.1007/978-1-4757-0163-0. |
[11] |
P. Piret, Structure and constructions of cyclic convolutional codes, IEEE Trans. Inf. Theory, 22 (1976), 147-155.
doi: 10.1109/TIT.1976.1055531. |
show all references
References:
[1] |
S. Estrada, J. R. García-Rozas, J. Peralta and E. Sánchez-García, Group convolutional codes, Adv. Math. Commun., 2 (2008), 83-94.
doi: 10.3934/amc.2008.2.83. |
[2] |
G. D. Forney Jr., Convolutional codes I: Algebraic structure, IEEE Trans. Inf. Theory, 16 (1970), 720-738,
doi: 10.1109/TIT.1970.1054541. |
[3] |
H. Gluesing-Luerssen and W. Schmale, On cyclic convolutional codes, Acta Appl. Math., 82 (2004), 183-237.
doi: 10.1023/B:ACAP.0000027534.61242.09. |
[4] |
J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Ideal codes over separable ring extensions, preprint, arXiv:1408.1546 |
[5] |
J. Gómez-Torrecillas, F. J. Lobillo and G. Navarro, Cyclic convolutional codes over separable extensions, in Coding Theory and Applications (eds. R. Pinto, P. Rocha Malonek and P. Vettori), Springer, 2015, 209-215.
doi: 10.1007/978-3-319-17296-5_22. |
[6] |
K. Hirata and K. Sugano, On semisimple extensions and separable extensions over non commutative rings, J. Math. Soc. Japan, 18 (1966), 360-373.
doi: 10.2969/jmsj/01840360. |
[7] |
R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge Univ. Press, 1994.
doi: 10.1017/CBO9780511840371. |
[8] |
N. Jacobson, Basic Algebra: II, W. H. Freeman Company, 1980. |
[9] |
S. R. López-Permouth and S. Szabo, Convolutional codes with additional algebraic structure, J. Pure Appl. Algebra, 217 (2013), 958-972.
doi: 10.1016/j.jpaa.2012.09.017. |
[10] |
R. Pierce, Associative Algebras, Springer-Verlag, 1982,
doi: 10.1007/978-1-4757-0163-0. |
[11] |
P. Piret, Structure and constructions of cyclic convolutional codes, IEEE Trans. Inf. Theory, 22 (1976), 147-155.
doi: 10.1109/TIT.1976.1055531. |
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