Distribution of trace values and two-weight, self-orthogonal codes over GF(p, 2)

Authors:
N. Pinnawala;A. Rao;T. A. Gulliver
Affiliations:
School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, Australia;School of Mathematical and Geospatial Sciences, RMIT University, Melbourne, VIC, Australia;Department of Electrical and Computer Engineering, University of Victoria, Victoria, B.C., Canada
Venue:
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2007

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Abstract

The uniform distribution of the trace map lends itself very well to the construction of binary and non-binary codes from Galois fields and Galois rings. In this paper we study the distribution of the trace map with the argument ax2 over the Galois field GF(p, 2). We then use this distribution to construct two-weight, self-orthogonal, trace codes.