On optimal linear codes of dimension 4
In coding theory, the problem of finding the shortest linear codes for a fixed set of parameters is central. Given the dimension $k$, the minimum weight $d$, and the order $q$ of the finite field $\bF_q$ over which the code is defined, the function $n_q(k, d)$ specifies the smallest length $n$ for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Yildiz Technical University
2021-05-01
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| Series: | Journal of Algebra Combinatorics Discrete Structures and Applications |
| Subjects: | |
| Online Access: | https://jacodesmath.com/index.php/jacodesmath/article/view/119 |
| Summary: | In coding theory, the problem of finding the shortest linear codes for a fixed set of parameters is central. Given the dimension $k$, the minimum weight $d$, and the order $q$ of the finite field $\bF_q$ over which the code is defined, the function $n_q(k, d)$ specifies the smallest length $n$ for which an $[n, k, d]_q$ code exists. The problem of determining the values of this function is known as the problem of optimal linear codes. Using the geometric methods through projective geometry, we determine $n_q(4,d)$ for some values of $d$ by constructing new codes and by proving the nonexistence of linear codes with certain parameters.
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| ISSN: | 2148-838X |