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A linear code over GF(41) of length n is a subspace of vector space in GF(41)n where GF(41) is a finite field with 41 elements. Self-dual code is a kind of linear codes having the property that its parity-check matrix and the transpose of generator matrix are the same. A Euclidean self-dual code ove...
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| Main Author: | |
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| Format: | Final Project |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/17483 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | A linear code over GF(41) of length n is a subspace of vector space in GF(41)n where GF(41) is a finite field with 41 elements. Self-dual code is a kind of linear codes having the property that its parity-check matrix and the transpose of generator matrix are the same. A Euclidean self-dual code over GF(41) is self-dual code that define using Euclidean inner product over vector space of GF(41)n. A MDS (Maximum Distance Separable) code is a linear code which has maximum value of minimum distance than other linear codes with the same length and dimension. In this final project, we constructed new Euclidean self-dual MDS or near MDS code over GF(41) of length 12 and 14. We obtained 14 new Euclidean self-dual near MDS codes of length 14 and 48 new Euclidean self-dual near MDS codes of length 12 with new weight enumerators. |
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