Linear codes with complementary-duals (LCD codes) are linear codes that trivially intersect with their dual (Massey, 1992). In this paper, we study double circulant codes (DC codes), which are a special class of quasi-cyclic codes, over $ \mathbb{F}_4 $ that are LCD. The main techniques used are as follows: Chinese reminder theory (CRT) decomposition in the line of (Ling et al. 2001), explicit enumeration, and asymptotics. In particular, we show that the class of codes considered here is asymptotically good.
Citation: Hatoon Shoaib. Double circulant complementary dual codes over $ \mathbb{F}_4 $[J]. AIMS Mathematics, 2023, 8(9): 21636-21643. doi: 10.3934/math.20231103
Linear codes with complementary-duals (LCD codes) are linear codes that trivially intersect with their dual (Massey, 1992). In this paper, we study double circulant codes (DC codes), which are a special class of quasi-cyclic codes, over $ \mathbb{F}_4 $ that are LCD. The main techniques used are as follows: Chinese reminder theory (CRT) decomposition in the line of (Ling et al. 2001), explicit enumeration, and asymptotics. In particular, we show that the class of codes considered here is asymptotically good.
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Hatoon Shoaib. Double circulant complementary dual codes over $ \mathbb{F}_4 $[J]. AIMS Mathematics, 2023, 8(9): 21636-21643. doi: 10.3934/math.20231103
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