856 research outputs found
The weight distributions of irreducible cyclic codes of length 2m
AbstractLet m be a positive integer and q be an odd prime power. In this paper, the weight distributions of all the irreducible cyclic codes of length 2m over Fq are determined explicitly
Weights in Codes and Genus 2 Curves
We discuss a class of binary cyclic codes and their dual codes. The minimum
distance is determined using algebraic geometry, and an application of Weil's
theorem. We relate the weights appearing in the dual codes to the number of
rational points on a family of genus 2 curves over a finite field
The Weight Enumerator of Three Families of Cyclic Codes
Cyclic codes are a subclass of linear codes and have wide applications in
consumer electronics, data storage systems, and communication systems due to
their efficient encoding and decoding algorithms. Cyclic codes with many zeros
and their dual codes have been a subject of study for many years. However,
their weight distributions are known only for a very small number of cases. In
general the calculation of the weight distribution of cyclic codes is heavily
based on the evaluation of some exponential sums over finite fields. Very
recently, Li, Hu, Feng and Ge studied a class of -ary cyclic codes of length
, where is a prime and is odd. They determined the weight
distribution of this class of cyclic codes by establishing a connection between
the involved exponential sums with the spectrum of Hermitian forms graphs. In
this paper, this class of -ary cyclic codes is generalized and the weight
distribution of the generalized cyclic codes is settled for both even and
odd alone with the idea of Li, Hu, Feng, and Ge. The weight distributions
of two related families of cyclic codes are also determined.Comment: 13 Pages, 3 Table
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