57,434 research outputs found
A class of narrow-sense BCH codes over of length
BCH codes with efficient encoding and decoding algorithms have many
applications in communications, cryptography and combinatorics design. This
paper studies a class of linear codes of length over
with special trace representation, where is an odd prime
power. With the help of the inner distributions of some subsets of association
schemes from bilinear forms associated with quadratic forms, we determine the
weight enumerators of these codes. From determining some cyclotomic coset
leaders of cyclotomic cosets modulo , we prove
that narrow-sense BCH codes of length with designed distance
have the corresponding trace representation, and have the
minimal distance and the Bose distance , where
Weight hierarchies of a family of linear codes associated with degenerate quadratic forms
We restrict a degenerate quadratic form over a finite field of odd
characteristic to subspaces. Thus, a quotient space related to is
introduced. Then we get a non-degenerate quadratic form induced by over the
quotient space. Some related results on the subspaces and quotient space are
obtained. Based on this, we solve the weight hierarchies of a family of linear
codes related to Comment: 12 page
A Class of Three-Weight Cyclic Codes
Cyclic codes are a subclass of linear codes and have applications in consumer
electronics, data storage systems, and communication systems as they have
efficient encoding and decoding algorithms. In this paper, a class of
three-weight cyclic codes over \gf(p) whose duals have two zeros is
presented, where is an odd prime. The weight distribution of this class of
cyclic codes is settled. Some of the cyclic codes are optimal. The duals of a
subclass of the cyclic codes are also studied and proved to be optimal.Comment: 11 Page
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