Constant weight codes (CWCs) and constant composition codes (CCCs) are two important classes of codes that have been studied extensively in both combinatorics and coding theory for nearly sixty years. In this paper we show that for all fixed odd distances, there exist near-optimal CWCs and CCCs asymptotically achieving the classic Johnson-type upper bounds.

中文翻译：

---

近似广义 Steiner 系统和近乎最优的恒重码


恒定权重代码 （CWC） 和恒定组合代码 （CCC） 是两类重要的代码，在组合学和编码理论中已经进行了近 60 年的广泛研究。在本文中，我们表明，对于所有固定奇数距离，存在近乎最优的 CWC 和 CCC 渐近达到经典的 Johnson 型上限。