誤り訂正符号概説(10周年記念号)

概要

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This paper presents the outlines of elementary error-correcting codes. The first section is an introductory representation. The Hamming weight and the Hamming distance are fundamental measurs for linear codes. They are introduced in the second section. Examples of Hamming single-error-detecting code, single-error-correcting code, and double-error-detecting code are illustrated in Table 2.1,2.3 and 2.4. respectively The third section provides the fundamental theories of finite groups, finite rings, Garois fields, vector spaces and matrixes. These mathematics are indispensable to the theories of error-correcting linear codes. If U is a linear code, and is also closed under the cyclic shift, then it is called a cyclic code. Examples of an encoding circuit and of a decoding circuit are illustrated in Fig.4.1 and Fig.4.2 respectively of the fourth section. In the fifth section, burst-error-correcting codes are investigated in some detail. Fig.5 shows the code-point-distribution on the (g, r) plane. The sixth section describes the convolutional code in short. This type of code is also useful for burst-error-collection.
四国大学の論文
2004-12-25