This study discusses the basis of a polynomial space generated by the weight enumerators of linear codes over GF(4) for several lengths, namely 2, 4, 6, 8, and 10. The results of the study show that each set of weight counters forms a space with dimensions that depend on the length of the code, namely 1, 1, 2, 4, and 5. This shows that the longer the code, the larger the dimensions of the space obtained.
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