Multilayer crisscross error and erasure correction

Martínez-Peñas, Umberto

doi:10.48550/arxiv.2203.07238

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Generic Decoding In the Cover Metric1

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2022

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“…From Theorem 23 we get a lower bound on the size of the spheres, which is of a similar form as the upper bound given in [16].…”

Section: Generic Decoding In the Cover Metricmentioning

confidence: 52%

Generic Decoding in the Cover Metric

Bitzer¹,

Renner²,

Wachter-Zeh³

et al. 2022

Preprint

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In this paper, we study the hardness of decoding a random code endowed with the cover metric. As the cover metric lies in between the Hamming and rank metric, it presents itself as a promising candidate for code-based cryptography. We give a polynomial-time reduction from the classical Hamming-metric decoding problem, which proves the NP-hardness of the decoding problem in the cover metric. We then provide a generic decoder, following the information set decoding idea from Prange's algorithm in the Hamming metric. A study of its cost then shows that the complexity is exponential in the number of rows and columns, which is in contrast to the behaviour in the Hamming metric, where the complexity grows exponentially in the number of code symbols.

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“…From Theorem 23 we get a lower bound on the size of the spheres, which is of a similar form as the upper bound given in [16].…”

Section: Generic Decoding In the Cover Metricmentioning

confidence: 52%