This paper presents a new achievable scheme for coded caching systems with $\mathsf{N}$ files, $\mathsf{K}=\mathsf{N}$ users, and cache size $\mathsf{M}=1/(\mathsf{N}-1)$. The scheme employs linear coding during the cache placement phase, and a three-stage transmissions designed to eliminate interference in the delivery phase. The achievable load meets a known converse bound, which impose no constraint on the cache placement, and is thus optimal. This new result, together with known inner and outer bounds, shows optimality of linear coding placement for $\mathsf{M} \leq 1/(\mathsf{N}-1)$ when $\mathsf{K}=\mathsf{N}\geq 3$. Interestingly and surprisingly, the proposed scheme is relatively simple but requires operations on a finite field of size at least 3.

翻译：本文针对包含$\mathsf{N}$个文件、$\mathsf{K}=\mathsf{N}$个用户及缓存容量$\mathsf{M}=1/(\mathsf{N}-1)$的编码缓存系统，提出一种新的可达方案。该方案在缓存放置阶段采用线性编码，并设计三阶段传输以消除交付阶段的干扰。其可达负载满足已知的对偶界（该对偶界对缓存放置无约束），因此具有最优性。结合现有内界与外界结果，这一新结论表明：当$\mathsf{K}=\mathsf{N}\geq 3$且$\mathsf{M} \leq 1/(\mathsf{N}-1)$时，线性编码放置具有最优性。有趣且令人意外的是，所提方案虽相对简单，但需在至少含3个元素的有限域上执行运算。