A construction for optimal SEFCCs on the Hamming code membership function is given by reducing distance-2 pair minimization to a max-cut problem solved via eigenvectors of distance-4 graphs, with optimality for even n attained by bent functions.
Function-correcting codes with optimal data protection for Hamming code membership
3 Pith papers cite this work. Polarity classification is still indexing.
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cs.IT 3years
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Generalized function-correcting partition codes unify protection for multiple message partitions with varying distance requirements and can achieve strictly lower redundancy than summing individual protections or using the strongest single code.
Linear codes qualify as strict function-correcting codes with data protection precisely when the subcode generated by their minimum-weight codewords is proper, with chain codes and narrow-sense BCH codes of designed distance three serving as infinite families that satisfy the condition.
citing papers explorer
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Function-Correction with Optimal Data Protection for the General Hamming Code Membership
A construction for optimal SEFCCs on the Hamming code membership function is given by reducing distance-2 pair minimization to a max-cut problem solved via eigenvectors of distance-4 graphs, with optimality for even n attained by bent functions.
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Generalized Function-Correcting Partition Codes
Generalized function-correcting partition codes unify protection for multiple message partitions with varying distance requirements and can achieve strictly lower redundancy than summing individual protections or using the strongest single code.
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Existence and Constructions of Strict Function-Correcting Codes with Data Protection
Linear codes qualify as strict function-correcting codes with data protection precisely when the subcode generated by their minimum-weight codewords is proper, with chain codes and narrow-sense BCH codes of designed distance three serving as infinite families that satisfy the condition.