Asymmetric Single Magnitude Four Error Correcting Codes

03/04/2019

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by   Derong Xie, et al.

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Limited magnitude asymmetric error model is well suited for flash memory. In this paper, we consider the construction of asymmetric codes correcting single error over Z_2^kr and which are based on so called B_1[4](2^kr) set. In fact, we reduce the construction of a maximal size B_1[4](2^kr) set for k≥3 to the construction of a maximal size B_1[4](2^k-3r) set. Finally, we give a explicit formula of a maximal size B_1[4](4r) set and some lower bounds of a maximal size B_1[4](2r) set. By computer searching up to q≤106, we conjecture that those lower bounds are tight.