Motivated by applications in DNA-based storage, we study explicit encoding and decoding schemes of binary strings satisfying locally balanced constraints, where the $(\ell,\delta)$-locally balanced constraint requires that the weight of any consecutive substring of length $\ell$ is between $\frac{\ell}{2}-\delta$ and $\frac{\ell}{2}+\delta$. In this paper we present coding schemes for the strongly locally balanced constraints and the locally balanced constraints, respectively. Moreover, we introduce an additional result on the linear recurrence formula of the number of binary strings which are $(6,1)$-locally balanced, as a further attempt to both capacity characterization and new coding strategies for locally balanced constraints.

翻译：我们研究明确的二进制编码和解码办法,以满足当地平衡的制约。 美元(ell,\delta)美元-当地平衡的制约要求长度($)美元(ell)美元-当地平衡的任何连续子字符串的权重在$(frac\ell)2美元-delta美元和$(frac)2 ⁇ 2 ⁇ delta美元之间的权重。我们在本文件中分别介绍了当地平衡的制约和当地平衡的制约的编码办法。此外,我们增加了一个结果,即双进制数量($6,1美元-地方平衡)的线性重复公式,以进一步尝试对当地平衡的限制进行能力定性和新的编码战略。