PERFECT CODES IN THE HOMOGENEOUS METRIC
Sign Up to like & getrecommendations! Published in 2025 at "Bulletin of the Australian Mathematical Society"
DOI: 10.1017/s0004972725100567
Abstract: We study perfect codes in the homogeneous metric over the ring $\mathbb {Z}_{{2}^k}, k\ge 2$ . We derive arithmetic nonexistence results from Diophantine equations on the parameters resulting from the sphere packing conditions, and a… read more here.
Keywords: homogeneous metric; perfect codes; codes homogeneous;
Perfect Codes Correcting a Single Burst of Limited-Magnitude Errors
Sign Up to like & getrecommendations! Published in 2023 at "IEEE Transactions on Information Theory"
DOI: 10.1109/tit.2022.3213239
Abstract: Motivated by applications to DNA-storage, flash memory, and magnetic recording, we study perfect burst-correcting codes for the limited-magnitude error channel. These codes are lattices that tile the integer grid with the appropriate error ball. We… read more here.
Keywords: limited magnitude; codes correcting; perfect codes; correcting single ... See more keywords
On q-ary Propelinear Perfect Codes Based on Regular Subgroups of the General Affine Group
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DOI: 10.1134/s0032946022010045
Abstract: A code is said to be propelinear if its automorphism group contains a subgroup acting on its codewords regularly. A subgroup of the group $$GA(r,q)$$ of affine transformations is said to be regular if it acts… read more here.
Keywords: perfect codes; ary propelinear; affine; propelinear perfect ... See more keywords
The Perfect Codes of Non-coprime and Coprime Graphs
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DOI: 10.46793/kgjmat2506.913t
Abstract: In this paper, we focus on the perfect and total perfect codes of the non-coprime and coprime graphs associated to the dihedral groups and finite Abelian groups. We used the advantage of independent sets and… read more here.
Keywords: codes non; perfect codes; non coprime; coprime coprime ... See more keywords