<![CDATA[This thesis explores the use of Jacobi polynomials and t-design properties in linear codes. The primary goal of the research is to develop a Python and SageMath program to compute the Jacobi polynomial for linear codes with multiple reference vectors. The methodology involves analyzing self-dual codes over various f ields to derive Jacobi polynomials under specific conditions. The results indicate that the analyzed codes do not satisfy the t-design criteria, as different random reference vectors yield varying Jacobi polynomials. The study offers insights into the relationship between linear codes and Jacobi polynomials, with suggestions for further exploration of more complex codes to meet the t-design criteria.]]>
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