Coding Theory and Number Theory (Mathematics and Its - download pdf or read online

By T. Hiramatsu,Günter Köhler

This ebook grew out of our lectures given within the Oberseminar on 'Cod­ ing concept and quantity idea' on the arithmetic Institute of the Wiirzburg college in the summertime Semester, 2001. The coding the­ ory combines mathematical splendor and a few engineering difficulties to an strange measure. the key good thing about learning coding conception is the great thing about this actual mix of arithmetic and engineering. during this e-book we want to introduce a few useful difficulties to the mathematics­ ematician and to deal with those as a vital a part of the improvement of recent quantity idea. The e-book includes 5 chapters and an appendix. bankruptcy 1 could typically be dropped from an introductory process linear codes. In Chap­ ter 2 we speak about a few family members among the variety of recommendations of a diagonal equation over finite fields and the burden distribution of cyclic codes. bankruptcy three starts via reviewing a few uncomplicated proof from elliptic curves over finite fields and modular types, and exhibits that the burden distribution of the Melas codes is represented through the hint of the Hecke operators performing on the distance of cusp varieties. bankruptcy four is a scientific research of the algebraic-geometric codes. for a very long time, the examine of algebraic curves over finite fields was once the province of natural mathematicians. within the interval 1977 - 1982, V. D. Goppa came across an grand connection among the speculation 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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