Three-Weight and Five-Weight Linear Codes over Finite Fields
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Authors: P. KUMAR AND N. M. KHAN
DOI: 10.46793/KgJMat2403.345K
Abstract:
Recently, linear codes constructed from defining sets have been studied extensively. For an odd prime p, let Trem be the trace function from ????pm onto ????pe, where e is a divisor of m. In this paper, for the defining set D = {x ∈ ????pm∗ : Trem(x2 + x) = 0} = {d1,d2,…,dn} (say), we define a pe-ary linear code ????D by
![( m m m )
????D = {cx = Tr e (xd1 ), Tr e (xd2 ), ..., Tr e (xdn ) : x ∈ ????pm }](717a90c0b66ad5efa048d926a9adf03d0x.png)
![m-
e](717a90c0b66ad5efa048d926a9adf03d1x.png)
Keywords:
Linear code, weight distribution, Gauss sum, cyclotomic number, secret sharing.
References: