论文标题
与有限字母的混合代码上的界限
Bounds on Mixed Codes with Finite Alphabets
论文作者
论文摘要
混合代码是不同尺寸空间的笛卡尔产品中错误校正的代码，模型降低存储系统的模型很好。虽然先前已经研究了此类代码的代数属性（例如，完美代码的存在）或在无限制字母尺寸的情况下，我们专注于有限字母的情况，并将吉尔伯特·瓦尔沙莫夫（Gilbert-Varshamov）概括为gilbert-varshamov，sphhere-sphere-there-backing，elias-bassalygo，elias-bassalygo，首先是线性的，并限制了该设置。在后一种情况下，我们的证明也是第一个使用Navon和Samorodnitsky的傅立叶分析方法的非对称单字母$ q $ y-ary case的证明。
Mixed codes, which are error-correcting codes in the Cartesian product of different-sized spaces, model degrading storage systems well. While such codes have previously been studied for their algebraic properties (e.g., existence of perfect codes) or in the case of unbounded alphabet sizes, we focus on the case of finite alphabets, and generalize the Gilbert-Varshamov, sphere-packing, Elias-Bassalygo, and first linear programming bounds to that setting. In the latter case, our proof is also the first for the non-symmetric mono-alphabetic $q$-ary case using Navon and Samorodnitsky's Fourier-analytic approach.
