An Optimised Hoffman Algorithm for Testing Linear Code Equivalency

Abstract

The Hoffman’s algorithm to test equivalency of linear codes is one of the techniques that have been used over the years; it is achieved by a comparison of codewords of the linear codes. However, this comparison technique becomes ineffective in instances where it is applied to linear codes with larger dimensions as it requires much run time complexity, space and size in comparing the codewords of each linear code. This paper proposes an optimised algorithm for testing the equivalency of linear codes, specifically addressing the limitations of the Hoffman method. To assess and compare the efficiencies of the Hoffman algorithm and the optimised algorithm, a set of nine carefully selected linear codes were subjected to equivalency testing. The CPU runtime of both algorithms was recorded using the C++ chrono library. The recorded runtime data was then utilized to create a scatter plot, offering a visual representation of the contrasting trends in CPU runtime between the two algorithms. The plot clearly indicate exponential growth in CPU runtime for the Hoffman algorithm as the length and dimension of the linear codes increases, in contrast, the proposed algorithm showcased a minimal growth in CPU runtime, indicating its superior efficiency and optimised performance.