Weighted Hamming metric structures |
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Authors: | Bora Moon |
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Institution: | Department of Mathematics, Postech, 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk, Republic of Korea |
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Abstract: | It is known that the binary generalized Goppa codes are perfect codes for the weighted Hamming metrics. In this paper, we present the existence of a weighted Hamming metric that admits a binary Hamming code (resp. an extended binary Hamming code) to be perfect code. For a special weighted Hamming metric, we also give some structures of a 2-perfect code, show how to construct a 2-perfect linear code and obtain the weight distribution of a 2-perfect code from the partial information of the code. |
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Keywords: | Perfect code Weighted Hamming metric Weight distribution Hamming code Extended Hamming code |
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