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Quotients of orders in cyclic algebras and space-time codes
($\sigma,\delta$)-codes
1. | University of King Khalid, Abha, Saudi Arabia |
2. | Université d'Artois, Lille Nord de France, Rue Jean Souvraz, Lens, 62300, France |
References:
[1] |
S. A. Amitsur, Derivations in simple rings, Proc. London Math. Soc., 3 (1957), 87-112. |
[2] |
D. Boucher, W. Geiselmann and F. Ulmer, Skew-cyclic codes, Appl. Algebra Engin. Commun. Comp., 18 (2007), 379-389.
doi: 10.1007/s00200-007-0043-z. |
[3] |
D. Boucher, P. Solé and F. Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
[4] |
D. Boucher and F. Ulmer, Linear codes using skew polynomials with automorphisms and derivations, Des. Codes Cryptogr., to appear.
doi: 10.1007/s10623-012-9704-4. |
[5] |
J. Delenclos and A. Leroy, Noncommutative symmetric functions and W-polynomials, J. Algebra Appl., 6 (2007), 815-837.
doi: 10.1142/S021949880700251X. |
[6] |
M. Giesbrecht, Factoring in skew polynomial rings over finite fields, J. Symb. Comp., 26 (1998), 463-468.
doi: 10.1006/jsco.1998.0224. |
[7] |
N. Jacobson, On pseudo linear transformations, Ann. Math., 38 (1937), 484-507.
doi: 10.2307/1968565. |
[8] |
S. K. Jain and S. R. Nagpaul, Topics in Applied Abstract Algebra, AMS, 2005. |
[9] |
T. Y. Lam and A. Leroy, Wedderburn polynomials over division rings, I, J. Pure Appl. Algebra, 186 (2004), 43-76.
doi: 10.1016/S0022-4049(03)00125-7. |
[10] |
T. Y. Lam, A. Leroy and A. Ozturk, Wedderburn polynomial over division rings, II, Contemp. Math., 456 (2008), 73-98.
doi: 10.1090/conm/456/08885. |
[11] |
A. Leroy, Pseudo-linear transformation and evaluation in Ore extension, Bull. Belg. Math. Soc., 2 (1995), 321-345. |
[12] |
A. Leroy, Noncommutative polynomial maps, J. Algebra Appl., 11 (2012).
doi: 10.1142/S0219498812500764. |
[13] |
S. R. López-Permouth and S. Szabo, Convolutional codes with additional algebraic structures, J. Pure Appl. Algebra, (2012).
doi: 10.1016/j.jpaa.2012.09.017. |
[14] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1978. |
[15] |
P. Solé, Codes over rings, in Proceeding of the CIMPA Summer School, Ankara, Turkey, 2008.
doi: 10.1109/TIT.2013.2277721. |
[16] |
P. Solé and O. Yemen, Binary quasi-cyclic codes of index 2 and skew polynomial rings, Finite Fields Appl., 18 (2012), 685-699.
doi: 10.1016/j.ffa.2012.02.002. |
[17] |
J. Wood, Code equivalence characterizes finite Frobenius rings, Proc. Amer. Math. Soc., 136 (2008), 699-706.
doi: 10.1090/S0002-9939-07-09164-2. |
show all references
References:
[1] |
S. A. Amitsur, Derivations in simple rings, Proc. London Math. Soc., 3 (1957), 87-112. |
[2] |
D. Boucher, W. Geiselmann and F. Ulmer, Skew-cyclic codes, Appl. Algebra Engin. Commun. Comp., 18 (2007), 379-389.
doi: 10.1007/s00200-007-0043-z. |
[3] |
D. Boucher, P. Solé and F. Ulmer, Skew constacyclic codes over Galois rings, Adv. Math. Commun., 2 (2008), 273-292.
doi: 10.3934/amc.2008.2.273. |
[4] |
D. Boucher and F. Ulmer, Linear codes using skew polynomials with automorphisms and derivations, Des. Codes Cryptogr., to appear.
doi: 10.1007/s10623-012-9704-4. |
[5] |
J. Delenclos and A. Leroy, Noncommutative symmetric functions and W-polynomials, J. Algebra Appl., 6 (2007), 815-837.
doi: 10.1142/S021949880700251X. |
[6] |
M. Giesbrecht, Factoring in skew polynomial rings over finite fields, J. Symb. Comp., 26 (1998), 463-468.
doi: 10.1006/jsco.1998.0224. |
[7] |
N. Jacobson, On pseudo linear transformations, Ann. Math., 38 (1937), 484-507.
doi: 10.2307/1968565. |
[8] |
S. K. Jain and S. R. Nagpaul, Topics in Applied Abstract Algebra, AMS, 2005. |
[9] |
T. Y. Lam and A. Leroy, Wedderburn polynomials over division rings, I, J. Pure Appl. Algebra, 186 (2004), 43-76.
doi: 10.1016/S0022-4049(03)00125-7. |
[10] |
T. Y. Lam, A. Leroy and A. Ozturk, Wedderburn polynomial over division rings, II, Contemp. Math., 456 (2008), 73-98.
doi: 10.1090/conm/456/08885. |
[11] |
A. Leroy, Pseudo-linear transformation and evaluation in Ore extension, Bull. Belg. Math. Soc., 2 (1995), 321-345. |
[12] |
A. Leroy, Noncommutative polynomial maps, J. Algebra Appl., 11 (2012).
doi: 10.1142/S0219498812500764. |
[13] |
S. R. López-Permouth and S. Szabo, Convolutional codes with additional algebraic structures, J. Pure Appl. Algebra, (2012).
doi: 10.1016/j.jpaa.2012.09.017. |
[14] |
F. J. MacWilliams and N. J. A. Sloane, The Theory of Error Correcting Codes, North-Holland, Amsterdam, 1978. |
[15] |
P. Solé, Codes over rings, in Proceeding of the CIMPA Summer School, Ankara, Turkey, 2008.
doi: 10.1109/TIT.2013.2277721. |
[16] |
P. Solé and O. Yemen, Binary quasi-cyclic codes of index 2 and skew polynomial rings, Finite Fields Appl., 18 (2012), 685-699.
doi: 10.1016/j.ffa.2012.02.002. |
[17] |
J. Wood, Code equivalence characterizes finite Frobenius rings, Proc. Amer. Math. Soc., 136 (2008), 699-706.
doi: 10.1090/S0002-9939-07-09164-2. |
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