Let $ M_{2}(\mathbb{F}_{2}) $ be the ring of matrices of order $ 2 \times 2 $ over finite field $ \mathbb{F}_{2} $ and $ \omega\in M_{2}(\mathbb{F}_{2}) $ be a cubic primitive root of unity. For any even positive integer $ t $, the weight distributions of the skew cyclic codes of length $ 3t $ with parity check polynomials $ x^{t}-\omega^{i}, i = 0, \; 1, \; 2 $ and $ (x^{t}-\omega^{j}) (x^{t}-\omega^{k}) $, $ 0 \le j < k\leq 2 $ were determined.
Citation: Zhen Du, Chuanze Niu. Weight distributions of a class of skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $[J]. AIMS Mathematics, 2025, 10(5): 11435-11443. doi: 10.3934/math.2025520
Let $ M_{2}(\mathbb{F}_{2}) $ be the ring of matrices of order $ 2 \times 2 $ over finite field $ \mathbb{F}_{2} $ and $ \omega\in M_{2}(\mathbb{F}_{2}) $ be a cubic primitive root of unity. For any even positive integer $ t $, the weight distributions of the skew cyclic codes of length $ 3t $ with parity check polynomials $ x^{t}-\omega^{i}, i = 0, \; 1, \; 2 $ and $ (x^{t}-\omega^{j}) (x^{t}-\omega^{k}) $, $ 0 \le j < k\leq 2 $ were determined.
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Zhen Du, Chuanze Niu. Weight distributions of a class of skew cyclic codes over $ M_{2}(\mathbb{F}_{2}) $[J]. AIMS Mathematics, 2025, 10(5): 11435-11443. doi: 10.3934/math.2025520
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