Balanced generalized weight matrices are used to construct optimal constant weight codes that are monomially inequivalent to codes derived from the classical simplex codes. What’s more, these codes can be assumed to be generated entirely by \(\omega \)-shifts of a single codeword where \(\omega \) is a primitive element of a Galois field. Additional constant weight codes are derived by projecting onto subgroups of the alphabet sets. These too are shown to be optimal.

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关于从$$\omega $$ -循环平衡广义称重矩阵导出的最佳恒重代码

平衡广义权重矩阵用于构造最优恒重码，该码与从经典单纯形码导出的码单项不等价。更重要的是，可以假设这些代码完全由单个码字的\(\omega \)移位生成，其中\(\omega \)是伽罗瓦域的原始元素。通过投影到字母表集的子组来导出附加的恒重代码。这些也被证明是最佳的。