A Class of Distance-Optimal Binary Linear Codes With Flexible Parameters

Abstract

Binary linear codes with good parameters have wide applications in data storage, communications, and information security. Inspired by the idea proposed by Ding recently and based on the Boolean functions with bivariate polynomial representation in even number of variables, we construct a class of two-weight binary linear codes with length $(2^{k}-1)e$ , dimension $2k$ , and minimum distance $2^{k-1}(e-1)$ , where $k\ge 2$ and $e$ is an arbitrary integer with $2^{k}-k . The variable $e$ provides flexible tradeoff between the code length and minimal distance. We determine the weight distributions of all the generated binary linear codes and, most notably, mathematically prove that all these codes are distance-optimal with respect to the Griesmer bound.