The explicit construction of finite fields and the computation in finite fields are emphasised in particular the construction of irreducible polynomials and the normal basis of finite fields are included the essentials of galois rings are also presented. Lectures on finite fields and galois rings zhe xian wan c i nese academy of sciences china 111 quadratic forms over finite fields of characteristic not 2 249 141 examples of galois rings 309 142 structure of galois rings 313. Tures on finite fields and galois rings which will be referred as lectures in the following the lectures is based on a course on finite fields i gave at nankai university tianjin and a seminar on galois rings i conducted at suzhou university suzhou both in 2002 it has been used as a textbook for. Get this from a library lectures on finite fields and galois rings wan zhe xian this is a textbook for graduate and upper level undergraduate students in mathematics computer science communication engineering and other fields the explicit construction of finite fields and . The galois ring is the unique galois extension of of degree for instance is and is generalizing finite fields cf finite field these rings find applications in similar areas linear recurrences cyclic codes association schemes and character sums
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