Artinian-schreier, Expansion Of The Algebraic Function Field Riemann-roch, Accompanied By Space

In this article, we consider the construction of algebraic geometry codes. when q =4, Starting from the Weierstrass semi-group and intermittent, we can get the demension result of Riemann-Roch space of L(αQ₀ +βP_∞). Selecting the appropriate divisors from the table which fit Theorem 4.1 and its corollary, we reach Riemann-Roch spaces of these special divisors. Riemann-Roch Spaces of kinds of divisors attached to Artin-Schreier extensions of algebraic function fields are explicitely computed in this paper.As an application, AG codes of [54, 43][54, 41],[54, 39],[54, 48]are constructed over F₁₆ and their minimum design distances compare the classical ones,satisfing: There are more general applications, i.e, q can take any positive integer value, such as q =8,[4 62, 414] code over F6 4is computed, its minimum distance is 6. However, the classical is 0.In Section 1, the background and history about the related are given.In Section 2 and 3, we introduce some preliminary results, including basic concepts and some notations, meanwhile we present a simple description of the systems.In Section 4 and 5, we get the main results, i.e, considering the construction of algebraic geometry codes, Riemann-Roch Spaces of kinds of divisors attached to Artin-Schreier extensions of algebraic function fields are explicitely computed in this paper .