Several classes of projective few-weight linear codes and their applications

It is well-known that few-weight linear codes have better applications in secret sharing schemes \cite{JY2006,CC2005}.In particular, projective two-weight codes are very precious as they are closely related to finite projective spaces, strongly regular graphs and combinatorial designs \cite{RC1986,CD2018,P1972}. Here, we present the following two applications.Comment: arXiv admin note: text overlap with arXiv:2107.0244

Two classes of two-weight linear codes over finite fields

Let $p\equiv 1\pmod 4$ be a prime, $m$ a positive integer, $\frac{\phi(p^m)}2$ the multiplicative order of $2$ modulo $p^m$, and let $q = 2^{ \frac{\phi(p^m)}2}$, where $\phi(\cdot)$ is the Euler's function. In this paper, we construct two classes of linear codes over $\Bbb F_q$ and investigate their weight distributions. By calculating two classes of special exponential sums, the desired results are obtained