Maximum sum rank distance codes
This page lists some maximal sum rank distance codes with various lengths and the matrix size 2*2. For the constructions of MSRD codes, we refer to the following references.
U. MartÍnez-Peňas and S. Puchinger, Maximum sum-rank distance codes over finite chain rings, IEEE Transactions on Information Theory, early access, 2024.
U. MartÍnez-Peňas, New constructions of MSRD codes, arXiv:2402.03084, 2024.
H. Chen, New explicit linear sum-rank-metric codes, IEEE Transactions on Information Theory, vol. 69, no. 10, pp. 6303-6313, 2023.
Martínez-Peñas U. Skew and linearized Reed–Solomon codes and maximum sum rank distance codes over any division ring, Journal of Algebra, vol. 504, pp. 587-612, 2018.
Neri A. Twisted linearized Reed-Solomon codes: A skew polynomial framework. Journal of Algebra, vol. 609, pp. 792-839, 2022.
H. Lao, Y.M. Chee, H. Chen and V. K. Vu, New constructions for linear maximum sum-rank Distance codes, submitted, 2023.
E. Byrne, H. Gluesing-Luerssen and A. Ravagnani, Fundamental properties of sum-rank-metric codes, IEEE Transactions on Information Theory, vol. 67, no. 10, pp. 6456-6475, 2021.
Comparison of the parameters of some F_q-linear MSRD codes
VII.1,[7]
<=q^m+1
1
m
<=t
m(t-d_sr+1)
VII.2,[7]
-
-
-
2
∑_{i=2}^{t}m_in_i+m_1(n_1-1)
VII.3a,[7]
-
-
-
∑_{i=1}^{t}n_i
m_t
VII.4,[7]
t=t_1+t_2,t_2≤q+1
n_{t_1+1},...,n_t=1
m_{t_1+1},...,m_t=1
∑_{i=1}^{t_1}n_i+t_2-m_{t_1}+1
m_{t_1}
VII.5,[7]
t=t_1+t_2,t_2≤q^{\hat{m}}+1
n_{t_1+1},...,n_t=1
m_{t_1}=\hat{m}a,m_{t_1+1},...,m_t=\hat{m}
∑_{i=1}^{t_1}n_i+t_2-a+1
m_{t_1}
VII.6,[7]
t=s+m+2,s≤m+m(m-1)/2+1
1
m_i=m for i∈[s+1],m_i=1 for i∈[s+2,s+m+2]
s+2
m+1
Theorem 5.2 [3]
-
m_i=n_i for i∈[1,t]
m_{J-1}≥k,m_J≥∑{J+1}^t m_i^2
∑_{i=1}^{J-1}n_i+β,J∈[1,t],β∈[1,n_J]
∑_{i=J}^{t}m_i^2-m_J(β-1)
Theorem 4,[4]
t≤q-1
-
m
d_{sr}
m(N-d_{sr}+1)
Theorem 6.3, [5]
t≤q-1,(-1)^{kN}N_{ F_{q^m}/ F_{q}}(η)
m
m
d_{sr}
m(N-d_{sr}+1)
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