Algebraic resolutions via projective parametrizations and geometric identifications solve seven open problems on codes supporting designs, including existence criteria for ovoid codes and constructions of MDS codes yielding 5-designs.
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4 Pith papers cite this work. Polarity classification is still indexing.
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cs.IT 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.
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.
A new explicit infinite family of 2-quasi-perfect Lee codes is built from the set H_q in finite fields and connected to Li's graphs and finite Euclidean graphs.
citing papers explorer
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Algebraic Resolutions of Seven Open Problems on Cyclic and Negacyclic Codes Supporting Designs
Algebraic resolutions via projective parametrizations and geometric identifications solve seven open problems on codes supporting designs, including existence criteria for ovoid codes and constructions of MDS codes yielding 5-designs.
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Intermediate Constacyclic Codes and Scalar-Residue Reed--Muller Layers
Proves that the minimum distance of intermediate constacyclic codes C(q,m,r,ℓ) equals a specific piecewise formula and determines the minimum affine support for non-terminal scalar-residue layers of generalized Reed-Muller codes.
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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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$2$-quasi-perfect Lee codes and abelian Ramanujan graphs: a new construction and relationship
A new explicit infinite family of 2-quasi-perfect Lee codes is built from the set H_q in finite fields and connected to Li's graphs and finite Euclidean graphs.