We establish a complete classification of binary group codes with complementary duals for a finite group and explicitly determine the number of linear complementary dual (LCD) cyclic group codes by using cyclotomic cosets. The dimension and the minimum distance for LCD group codes are explored. Finally, we find a connection between LCD MDS group codes and maximal ideals.
翻译:我们为一定的组群建立完全的二元组群码分类,配有补充性双重代码,并通过使用环形共合物,明确确定线性补充性双环形组群群码的数目,探讨液态组群码的尺寸和最小距离。最后,我们发现LCD MDS组群码和最大理想之间的联系。