說明 
54 p 
附註 
Source: Masters Abstracts International, Volume: 5006, 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 xnx over F. Each factor then gives us a cyclic code of some dimension k over F 

Constructing factorizations of xn1 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 5006

主題 
Mathematics


0405

Alt Author 
East Carolina University. Mathematics

