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On character sums and codes

โœ Scribed by Hannu Tarnanen

Publisher
Elsevier Science
Year
1985
Tongue
English
Weight
523 KB
Volume
57
Category
Article
ISSN
0012-365X

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โœฆ Synopsis

Coding-theoretical methods are used to obtain improved lower bounds for character sums induced by a multiplicative character of an arbitrary order over GF(q).

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Let f be a complex-valued function on a finite field F such that f(0)=0, f(1)=1, and |f(x)|=1 for x ] 0. H. Cohn asked if it follows that f is a nontrivial multiplicative character provided that ; x ยฅ F f(x) f(x+h)=-1 for h ] 0. We prove that this is the case for finite fields of prime cardinality u