Titlebook: Selected Unsolved Problems in Coding Theory; David Joyner,Jon-Lark Kim Textbook 2011 Springer Science+Business Media, LLC 2011 Assmus–Matt

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e they can enjoy high quality data storage and computing services in a ubiquitous manner. This is known as the outsourcing computation paradigm. Recently, the problem for securely outsourcing various expensive computations or storage has attracted considerable attention in the academic community. In

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Springer Science+Business Media, LLC 2011

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The Riemann Hypothesis and Coding Theory,The Duursma zeta function is the coding-theoretic analog of the Artin–Weil zeta function of an algebraic curve over a finite field. This chapter explores some of the fascinating properties and conjectures surrounding the Duursma zeta function. Numerous computational examples are given.

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Codes from Modular Curves,st remarkable applications of algebraic geometry to coding theory arise from these modular curves. It turns out these algebraic-geometric codes (“AG codes”) constructed from modular curves can have parameters which beat the Gilbert–Varshamov lower bound if the ground field is sufficiently large.

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Textbook 2011archers in algebraic coding theory, especially those who are interested in finding some current unsolved problems. Familiarity with concepts in algebra, number theory, and modular forms is assumed. The work may be used as supplementary reading material in a graduate course on coding theory or for self-study..