On optimal linear codes of dimension 4

Yıl 2021, , 73 - 90, 20.05.2021

Nanami Bono Maya Fujii Tatsuya Maruta

https://doi.org/10.13069/jacodesmath.935947

Cited By: 1

Öz

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.

Anahtar Kelimeler

Optimal linear codes, Griesmer bound, Geometric method

Kaynakça

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