Manuel González-Sarabia, Humberto Muñoz-George, Jorge A. Ordaz, Eduardo Sáenz-de-Cabezón, Rafael H. Villarreal
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引用次数: 0
Abstract
For projective Reed–Muller-type codes we give a global duality criterion in terms of the v-number and the Hilbert function of a vanishing ideal. As an application, we provide a global duality theorem for projective Reed–Muller-type codes over Gorenstein vanishing ideals, generalizing the known case where the vanishing ideal is a complete intersection. We classify self dual Reed–Muller-type codes over Gorenstein ideals using the regularity and a parity check matrix. For projective evaluation codes, we give a duality theorem inspired by that of affine evaluation codes. We show how to compute the regularity index of the r-th generalized Hamming weight function in terms of the standard indicator functions of the set of evaluation points.
对于射影里德-穆勒型码，我们给出了一个以消失理想的 v 数和希尔伯特函数为基础的全局对偶准则。作为应用，我们提供了戈伦斯坦消失理想上的射影里德-穆勒型码的全局对偶定理，推广了消失理想是完全交集的已知情况。我们利用正则性和奇偶校验矩阵对 Gorenstein 理想上的自对偶 Reed-Muller 型编码进行了分类。对于射影评价码，我们给出了一个受仿射评价码启发的对偶性定理。我们展示了如何根据评价点集合的标准指示函数计算 r 次广义汉明权重函数的正则性指数。
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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