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- W4386869659 abstract "A code <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>C</i> is called <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z<sub>p</sub>Z<sub>p<sup>2</sup></sub></i> -linear if it is the Gray image of a <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z<sub>p</sub>Z<sub>p<sup>2</sup></sub></i> -additive code. For any prime number <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>p</i> larger than 3, the bounds of the rank of <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z<sub>p</sub>Z<sub>p<sup>2</sup></sub></i> -linear codes are given. For each value of the rank and the pairs of rank and the dimension of the kernel of <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z<sub>p</sub>Z<sub>p<sup>2</sup></sub></i> -linear codes, we give detailed construction of the corresponding codes. As an example, the rank and the dimension of the kernel of <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z</i> <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>5</sub> <italic xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>Z</i> <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>25</sub> -linear codes are studied." @default.
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- W4386869659 date "2023-01-01" @default.
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- W4386869659 title "Rank and pairs of Rank and Dimension of Kernel of Z<sub> <i>p</i> </sub>Z<sub> <i>p</i> <sup>2</sup> </sub>-linear codes" @default.
- W4386869659 doi "https://doi.org/10.1109/tit.2023.3317064" @default.
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