New PDF release: Coding Theory and Number Theory (Mathematics and Its

By T. Hiramatsu,Günter Köhler

This publication grew out of our lectures given within the Oberseminar on 'Cod­ ing thought and quantity idea' on the arithmetic Institute of the Wiirzburg college in the summertime Semester, 2001. The coding the­ ory combines mathematical attractiveness and a few engineering difficulties to an strange measure. the key good thing about learning coding thought is the great thing about this actual mix of arithmetic and engineering. during this publication we want to introduce a few functional difficulties to the mathematics­ ematician and to deal with those as a vital a part of the improvement of contemporary quantity conception. The publication comprises 5 chapters and an appendix. bankruptcy 1 could regularly be dropped from an introductory process linear codes. In Chap­ ter 2 we talk about a few kin among the variety of strategies of a diagonal equation over finite fields and the burden distribution of cyclic codes. bankruptcy three starts off by means of reviewing a few simple proof from elliptic curves over finite fields and modular varieties, and indicates that the burden distribution of the Melas codes is represented by way of the hint of the Hecke operators performing on the distance of cusp kinds. bankruptcy four is a scientific learn of the algebraic-geometric codes. for a very long time, the research of algebraic curves over finite fields used to be the province of natural mathematicians. within the interval 1977 - 1982, V. D. Goppa chanced on an grand connection among the idea of algebraic curves over fi­ nite fields and the idea of q-ary codes.

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Coding Theory and Number Theory (Mathematics and Its Applications) by T. Hiramatsu,Günter Köhler

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