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Ideals of the Polynomial Ring for Error Control In Computer Applications

机译：多项式环在计算机应用中的错误控制的理想选择

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This research provides ideals of the polynomial ring associated with the code words of a cyclic code C. If the set of polynomials corresponding to codeword is given by me(c), an ideal of F, it can be shown that C is a cyclic code. Principal ideals of cyclic codes are defined from a new view point involving polynomials. The potentialities of these codes for error control in computer applications are described in detail. Error coding and decoding use mathematical formulas to encode data at the source into longer words for transmission. Performance of different types of error control codes has been investigated for application in computerized systems. Algebraic geometry over principal ideals of cyclic codes and their applications to error control are also discussed. A code region for optimal codes obtained has been constructed as predicted by Shannon’s Theorem.
机译：这项研究提供了与循环码C的代码字关联的多项式环的理想状态。如果与码字相对应的多项式集由me（c）给出，则理想值F可以证明C是循环码。从涉及多项式的新观点定义了循环码的主要理想。详细介绍了这些代码在计算机应用中用于错误控制的可能性。错误编码和解码使用数学公式将源处的数据编码为更长的字以进行传输。已经研究了不同类型的错误控制代码的性能，以用于计算机系统。还讨论了循环码的基本理想之上的代数几何及其在差错控制中的应用。如香农定理所预测的那样，获得了用于获得最佳代码的代码区域。

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