A Deterministic Dimension Property of Twisted Goppa Codes
Abstract
This paper presents a large-scale computational study on the dimensional properties of twisted Goppa codes. Through the systematic analysis of over 50,000 parameter sets, we uncover a remarkable deterministic regularity: the actual dimension k of a twisted Goppa code is uniquely determined by a set of macro-parameters (q,m,t,b,u). Specifically, when the order of the finite field q, the extension degree m, the degree t of the Goppa polynomial, the translation parameter b of the automorphism, and the order u of the transformation are fixed, the dimension k of the generated code remains constant.
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