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作者 Brame, Benjamin
書名 Idempotents in cyclic codes
國際標準書號 9781267338716
book jacket
說明 54 p
附註 Source: Masters Abstracts International, Volume: 50-06, page:
Adviser: Zachary Robinson
Thesis (M.A.)--East Carolina University, 2012
Cyclic codes give us the most probable method by which we may detect and correct data transmission errors. These codes depend on the development of advanced mathematical concepts. It is shown that cyclic codes, when viewed as vector subspaces of a vector space of some dimension n over some finite field F, can be approached as polynomials in a ring. This approach is made possible by the assumption that the set of codewords is invariant under cyclic shifts, which are linear transformations. Developing these codes seems to be equivalent to factoring the polynomial xn--x over F. Each factor then gives us a cyclic code of some dimension k over F
Constructing factorizations of xn--1 is accomplished by using cyclotomic polynomials and idempotents of the code algebra. The use of these two concepts together allows us to find cyclic codes in Fn. Hence, the development of cyclic codes is a journey from codewords and codes to fields and rings and back to codes and codewords
School code: 0600
Host Item Masters Abstracts International 50-06
主題 Mathematics
Alt Author East Carolina University. Mathematics
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