Abstract
This paper gives an important result on the existence of matrix representations of a finite field which are closed under transposition and not symmetric. A characterization of self-dual codes which areq-ary images of non self-dual codes is given.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Beenker, G. F. M.: A note on extended quadratic residue codes over GF(9) and their ternary images. IEEE Trans. Inform. Theory. IT.30(2), (1984)
Mouaha, C.: On cyclic codes which are q-ary images of linear codes, AAECC2, 163–170 (1992)
Mouaha, C.: Onq-ary images of self-dual codes. AAECC3, 311–319 (1992)
Donald Y., Goldberg: Reconstructing the ternary Golay code. J. Combinatorial Theory Ser.A42, 296–299 (1986)
Karlin, M., Bhargava, V. K., Tavares, S. E.: A note on extended quaternary quadratic residue codes and their binary images. Info. Control38, 148–153 (1978)
Seroussi, G., Lempel, A.: On symmetric representations of finite fields. SIAM J. ALG. Disc. Math.4(1), 14–21 (1983)
Weiss, A.: Characteristic polynomials of symmetric matrices. Preprint, Department of Maths, University of Alberta, Edmonton, Canada
Wolfmann, J. A.: A new construction of the binary Golay code [24, 12, 8] using a group algebra over a finite field. Discrete Math.31, 337–338 (1980)
Wolfmann, J.: Differents aspects de la démultiplication des codes. Traitement du signal,1(2), (1984)
Wolfmann, J.: A group algebra construction of binary even self-dual codes. Discrete Math.65 (1987)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mouaha, C. On asymmetric representations of GF(q m) and self-dual codes. AAECC 6, 81–87 (1995). https://doi.org/10.1007/BF01225645
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01225645