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Distribution of trace values and two-weight, self-orthogonal codes over GF\((p,2)\). (English) Zbl 1195.94080

Boztaş, Serdar (ed.) et al., Applied algebra, algebraic algorithms and error-correcting codes. 17th international symposium, AAECC-17, Bangalore, India, December 16–20, 2007. Proceedings. Berlin: Springer (ISBN 978-3-540-77223-1/pbk). Lecture Notes in Computer Science 4851, 311-320 (2007).
Summary: 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 \(ax ^{2}\) over the Galois field GF\((p,2)\). We then use this distribution to construct two-weight, self-orthogonal, trace codes.
For the entire collection see [Zbl 1133.94006].

MSC:

94B05 Linear codes (general theory)
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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References:

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