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Tilings with n-Dimensional Chairs and their Applications to Asymmetric\n Codes

2012/04/18 by Sarit Buzaglo, Tuvi Etzion, Buzaglo, Sarit +1
Computer Science · Engineering · #Cellular Automata and Applications #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1204.4204

openalex publication_date 2012/04/18 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

An n-dimensional chair consists of an n-dimensional box from which a\nsmaller n-dimensional box is removed. A tiling of an n-dimensional chair\nhas two nice applications in coding for write-once memories. The first one is\nin the design of codes which correct asymmetric errors with limited-magnitude.\nThe second one is in the design of n cells q-ary write-once memory codes.\nWe show an equivalence between the design of a tiling with an integer lattice\nand the design of a tiling from a generalization of splitting (or of Sidon\nsequences). A tiling of an n-dimensional chair can define a perfect code for\ncorrecting asymmetric errors with limited-magnitude. We present constructions\nfor such tilings and prove cases where perfect codes for these type of errors\ndo not exist.\n

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