Doubly and triply extended MSRD codes

Umberto Martínez-Peñas

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arXiv · 2212.05528

Doubly and triply extended MSRD codes

Umberto Martínez-Peñas

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Abstract

In this work, doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes are generalized. We obtain a general result in which we characterize when a multiply extended code for a general metric attains the Singleton bound. We then use this result to obtain several families of doubly extended and triply extended maximum sum-rank distance (MSRD) codes that include doubly extended linearized Reed--Solomon codes and triply extended Reed--Solomon codes as particular cases. To conclude, we discuss when these codes are one-weight codes.

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Umberto Martínez-Peñas. 2022-12-11. Doubly and triply extended MSRD codes. https://arxiv.org/abs/2212.05528

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