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All Two-Weight Irreducible Cyclic Codes?

✍ Scribed by Bernhard Schmidt; Clinton White

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
338 KB
Volume
8
Category
Article
ISSN
1071-5797

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✦ Synopsis

The aim of this paper is the classi"cation of two-weight irreducible cyclic codes. Using Fourier transforms and Gauss sums, we obtain necessary and su$cient numerical conditions for an irreducible cyclic code to have at most two weights. This gives a uni"ed explanation for all two-weight irreducible cyclic codes and allows a conjecturally complete classi"cation. Aside from the two known in"nite families of two-weight irreducible cyclic codes, a computer search reveals 11 sporadic examples. We conjecture that these are already all two-weight irreducible cyclic codes and give a partial proof of our conjecture conditionally on GRH.

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