For any given alphabet of size $q$, a Homopolymer Free code (HF code) refers to an $(n, M, d)_q$ code of length $n$, size $M$ and minimum Hamming distance $d$, where all the codewords are homopolymer free sequences. For any given alphabet, this work provides upper and lower bounds on the maximum size of any HF code using Sphere Packing bound and Gilbert-Varshamov bound. Further, upper and lower bounds on the maximum size of HF codes for various HF code families are calculated. Also, as a specific case, upper and lower bounds are obtained on the maximum size of homopolymer free DNA codes.

翻译：对于任意给定的字母表规模 $q$，同聚物自由编码（HF编码）是指一种长度为 $n$、规模为 $M$、最小汉明距离为 $d$ 的 $(n, M, d)_q$ 编码，其中所有码字均为同聚物自由序列。对于任意给定字母表，本工作利用球包界和吉尔伯特-瓦尔沙莫夫界给出了任意 HF 编码最大规模的上界与下界。此外，计算了不同 HF 编码族最大规模的上界与下界。同时，作为特例，本文获得了同聚物自由 DNA 编码最大规模的上界与下界。