Bounds and Genericity of Sum-Rank-Metric Codes
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We derive simplified sphere-packing and Gilbert-Varshamov bounds for codes in the sum-rank metric, which can be computed more efficently than previous ones.They give rise to asymptotic bounds that cover the asymptotic setting that has not yet been considered in the literature: families of sum-rank-metric codes whose block size grows in the code length. We also provide two genericity results: we show that random linear codes achieve almost the sum-rank-metric Gilbert-Varshamov bound with high probability. Furthermore, we derive bounds on the probability that a random linear code attains the sum-rank-metric Singleton bound, showing that for large enough extension field, almost all linear codes achieve it.
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