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• W3092149692 abstract "Motivated by the duplication-correcting problem for data storage in live DNA, we study the construction of constant-weight codes in $ell_1$-metric. By using packings and group divisible designs in combinatorial design theory, we give constructions of optimal codes over non-negative integers and optimal ternary codes with $ell_1$-weight $wleq 4$ for all possible distances. In general, we derive the size of the largest ternary code with constant weight $w$ and distance $2w-2$ for sufficiently large length $n$ satisfying $nequiv 1,w,-w+2,-2w+3pmod{w(w-1)}$." @default.
• W3092149692 created "2020-10-15" @default.
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• W3092149692 date "2020-03-01" @default.
• W3092149692 modified "2023-09-27" @default.
• W3092149692 title "Optimal codes with small constant weight in $ell_1$-metric" @default.
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