We study properties of binary runlength-limited sequences with additional restrictions on their weight and/or the number of runs of identical symbols they contain. An algebraic and a probabilistic (entropic) characterization of the exponential growth rate of the number of such sequences, i.e., their information capacity, are obtained, and properties of the capacity as a function of its parameters are stated. The second-order term in the asymptotic expansion of the rate of these sequences is also given, and the typical values of the relevant quantities are derived. Several applications of the results are illustrated, including bounds on codes for the run-preserving insertion-deletion channel in the fixed-number-of-errors regime, a sphere-packing bound for sparse-noise channels in the fixed-fraction-of errors regime, and the asymptotics of constant-weight sub-block constrained sequences. In addition, the asymptotics of a closely related notion -- $ q $-ary sequences with fixed Manhattan weight -- is briefly discussed, and an application in coding for molecular timing channels is illustrated.

翻译：我们研究二元长限序列的特性,同时对其重量和(或)所含有的相同符号的运行次数加以额外限制。我们研究了这些序列的二元长限序列的特性。我们获得了这些序列数量指数增长率的代数和概率(活性)特征,即其信息能力,并说明了其参数的函数特性。还给出了这些序列速度的无时势扩展的第二阶术语,并得出了相关数量的典型值。对结果的若干应用作了说明,包括固定数载体系统中运行保留插入式删除通道的代码的界限,固定折射系统中微小噪音通道的外层包装,以及固定重量子段受限序列的无序。此外,还简要讨论了一个密切相关的概念 -- -- 以美元计值为曼哈顿固定重量的序列 -- -- 的杂念,并展示了分子时间段的编码应用情况。