Groups Of Linear Isometries On Poset Structures

Let V be an n-dimensional vector space over a finite field Fq and P = { 1, 2, ..., n } a poset. We consider on V the poset-metric dP. In this paper, we give a complete description of groups of linear isometries of the metric space (V, dP), for any poset-metric dP. © 2007 Elsevier B.V. All rights reserved.3081841164123Ahn, J., Kim, H.K., Kim, J.S., Kim, M., Classification of perfect linear codes with crown poset structure (2003) Discrete Math., 268, pp. 21-30Brualdi, R., Graves, J.S., Lawrence, M., Codes with a poset metric (1995) Discrete Math., 147, pp. 57-72S.H. Cho, D.S. Kim, Automorphism group of the crown-weight space, submitted for publicationHyun, J.Y., Kim, H.K., The poset structures admitting the extended binary Hamming code to be a perfect code (2004) Discrete Math., 288, pp. 37-47Jang, Y., Park, J., On a MacWilliams type identity and a perfectness for a binary linear (n, n - 1, j)-poset code (2003) Discrete Math., 265, pp. 85-104D.S. Kim, Association schemes and MacWilliams dualities for generalized Rosenbloom-Tsfasman poset, submitted for publicationKim, D.S., Lee, J.G., A MacWilliams-type identity for linear codes on weak order (2003) Discrete Math., 262, pp. 181-194Lee, K., Automorphism group of the Rosenbloom-Tsfasman space (2003) European J. Combin., 24, pp. 607-612Lee, Y., Projective systems and perfect codes with a poset metric (2004) Finite Fields and Their Appl., 10, pp. 105-112Niederreiter, H., A combinatorial problem for vector spaces over finite fields (1991) Discrete Math., 96, pp. 221-228L. Panek, M. Firer, M. Muniz, Symmetry groups of Rosenbloom-Tsfasman spaces, submitted for publicationR. Stanley, Enumerative Combinatorics, vol. I, Wadsworth and Brooks/Cole, Monterey, CA, 1986Yu Rosenbloom, M., Tsfasman, M.A., Codes for the m-metric (1997) Problems Inform. Transmission, 33, pp. 45-5