Algebraic Geometry (AG) codes (i.e. linear codes from algebraic function fields) in the Hamming metric were proposed by Goppa in 1980 and have been intensively studied ever since. Linearized Algebraic Geometry codes, the analogue of AG codes in the sum-rank metric, were instead introduced more recently [9], using quotients of the ring of Ore polynomials with coefficients in an algebraic function field. In this paper, we further investigate the results in [9], providing explicit, optimal and asymptotic constructions.

翻译：代数几何（AG）码（即源自代数函数域的线性码）在汉明度量下由Goppa于1980年提出，此后得到了广泛深入的研究。而线性化代数几何码——AG码在求和秩度量下的类比——则于近期被引入[9]，其构造利用了系数取自代数函数域的Ore多项式环的商结构。本文进一步深化了文献[9]中的结果，提供了显式、最优且渐近的构造方案。