l_(1)度量下三元常重码的新进展

New results on ternary constant weight codes under l_(1)-metric

l_(1)度量下的常重码在活体DNA存储技术中有非常重要的应用.本文研究长度为n、l_(1)权重为w、最小l_(1)距离为2w-4的最优三元常重码的大小.对一般的n和w,本文给出码字个数的上界.当w=6时,本文利用计算代价的方式改进了上界,并通过构造码类给出下界.从而对所有奇数n≠9,13,17 (mod 20)分情形确定了最大码字个数在渐近意义下的精确值或n的一阶、二阶系数.

Constant weight codes under l_(1)-metric are important in the technology of storage in live DNA.In this paper,we study the size of optimal ternary constant weight codes with given length n,l_(1)-weight w and minimum l_(1)-distance 2w-4.For general n and w,we give an upper bound on the number of codewords in such a code.When w=6,we further improve the upper bound by computing the cost,and give lower bounds by constructions.In particular for all odd n≠9,13,17(mod 20),we determine the maximum number of codewords,or determine the first-or the second-order coefficients of n asymptotically in the maximum number formula.