COMPUTING THE DISTANCE DISTRIBUTION OF SYSTEMATIC NONLINEAR CODES

Abstract

The most important families of nonlinear codes are systematic. A brute-force check is the only known method to compute their weight distribution and distance distribution. On the other hand, it outputs also all closest word pairs in the code. In the black-box complexity model, the check is optimal among closest-pair algorithms. In this paper, we provide a Gröbner basis technique to compute the weight/distance distribution of any systematic nonlinear code. Also our technique outputs all closest pairs. Unlike the check, our method can be extended to work on code families.