Actas de congresos
Translation Association Schemes, Poset Metrics, And The Shape Enumerator Of Codes
Registro en:
9781467325790
Ieee International Symposium On Information Theory - Proceedings. , v. , n. , p. 101 - 105, 2012.
10.1109/ISIT.2012.6283005
2-s2.0-84867552617
Autor
Barg A.
Firer M.
Institución
Resumen
Poset metrics form a generalization of the Hamming metric on the space double-struck F q n. Orbits of the group of linear isometries of the space give rise to a translation association scheme. The structure of the dual scheme is important in studying duality of linear codes; this study is facilitated if the scheme is self-dual. We study the relation between self-duality of the scheme and that of the poset. We also give new examples of poset metric spaces and describe the association schemes that arise from linear isometries. © 2012 IEEE.
101 105 Barg, A., Purkayastha, P., Bounds on ordered codes and orthogonal arrays (2009) Moscow Mathematical Journal, 9 (2), pp. 211-243. , arXiv:cs/0702033 Brouwer, A.E., Cohen, A.M., Neumaier, A., (1989) Distance-regular Graphs, , Springer-Verlag, Berlin e. a Brualdi, R.A., Graves, J.S., Lawrence, K.M., Codes with a poset metric (1995) Discrete Math., 147 (1-3), pp. 57-72 Dougherty, S.T., Skriganov, M.M., MacWilliams duality and the Rosenbloom-Tsfasman metric (2002) Mosc. Math. J., 2 (1), pp. 81-97+199 Kim, D.S., Kim, H.K., Duality of Translation Association Schemes Coming from Certain Actions, , arXiv:1108.4947 Kim, H.K., Oh, D.Y., A classification of posets admitting the MacWilliams identity (2005) IEEE Trans. Inform. Theory, 51 (4), pp. 1424-1431 Lee, K., The automorphism group of a linear space with the Rosenbloom-Tsfasman metric (2003) Eur. J. Combinatorics, 24, pp. 607-612 Martin, W.J., Stinson, D.R., Association schemes for ordered orthogonal arrays and (T,M, S)-nets (1999) Canad. J. Math., 51 (2), pp. 326-346 Panek, L., Firer, M., Kim, H.K., Hyun, J.Y., Groups of linear isometries on poset structures (2008) Discrete Math., 308 (18), pp. 4116-4123 Park, W., Barg, A., Linear ordered codes, shape enumerators, and parallel channels Proc. 48th Annual Allerton Conf. Commun. Control Comput., Monticello, IL, Sept. 30-Oct. 1, 2010, pp. 361-367 Rosenbloom, M.Yu., Tsfasman, M.A., Codes for the m-metric (1997) Problems of Information Transmission, 33 (1), pp. 45-52