TY - GEN
T1 - Ideal structure of the silver code
AU - Ray, Avik
AU - Vinodh, K.
AU - Othman, G. Rekaya Ben
AU - Kumar, P. V.
PY - 2009/11/19
Y1 - 2009/11/19
N2 - The Silver code has captured a lot of attention in the recent past, because of its nice structure and fast decodability. In their recent paper, Hollanti et al. show that the Silver code forms a subset of the natural order of a particular cyclic division algebra (CDA). In this paper, the algebraic structure of this subset is characterized. It is shown that the Silver code is not an ideal in the natural order but a right ideal generated by two elements in a particular order of this CDA. The exact minimum determinant of the normalized Silver code is computed using the ideal structure of the code. The construction of Silver code is then extended to CDAs over other number fields.
AB - The Silver code has captured a lot of attention in the recent past, because of its nice structure and fast decodability. In their recent paper, Hollanti et al. show that the Silver code forms a subset of the natural order of a particular cyclic division algebra (CDA). In this paper, the algebraic structure of this subset is characterized. It is shown that the Silver code is not an ideal in the natural order but a right ideal generated by two elements in a particular order of this CDA. The exact minimum determinant of the normalized Silver code is computed using the ideal structure of the code. The construction of Silver code is then extended to CDAs over other number fields.
U2 - 10.1109/ISIT.2009.5205771
DO - 10.1109/ISIT.2009.5205771
M3 - Conference contribution
AN - SCOPUS:70449499119
SN - 9781424443130
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 2818
EP - 2822
BT - 2009 IEEE International Symposium on Information Theory, ISIT 2009
T2 - 2009 IEEE International Symposium on Information Theory, ISIT 2009
Y2 - 28 June 2009 through 3 July 2009
ER -