A correspondence is built between nondegenerate matrix rank-metric codes and geometric systems, producing Delsarte-type incidence identities plus applications to generalized weights and semifields.
Additive codes attaining the Griesmer bound
3 Pith papers cite this work. Polarity classification is still indexing.
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Pith papers citing it
abstract
Additive codes may have better parameters than linear codes. However, still very few cases are known and the explicit construction of such codes is a challenging problem. Here we show that a Griesmer type bound for the length of additive codes can always be attained with equality if the minimum distance is sufficiently large. This solves the problem for the optimal parameters of additive codes when the minimum distance is large and yields many infinite series of additive codes that outperform linear codes.
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math.CO 3verdicts
UNVERDICTED 3representative citing papers
b_2(5,2,2;s) is completely determined as a function of s via integer linear programming on the projective geometry PG(4,2), with additional bounds and constructions for other n_q and b_q parameters.
Optimal parameters of additive quaternary codes are settled for dimensions 3.5 and 4, plus the large-distance case in any dimension.
citing papers explorer
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The geometry of rank-metric codes
A correspondence is built between nondegenerate matrix rank-metric codes and geometric systems, producing Delsarte-type incidence identities plus applications to generalized weights and semifields.
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Generalized Hamming weights of additive codes and geometric counterparts
b_2(5,2,2;s) is completely determined as a function of s via integer linear programming on the projective geometry PG(4,2), with additional bounds and constructions for other n_q and b_q parameters.
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Optimal additive quaternary codes of dimension $3.5$ and $4$
Optimal parameters of additive quaternary codes are settled for dimensions 3.5 and 4, plus the large-distance case in any dimension.