Abstract We investigate unbiased weighing matrices of weight 9 and provide a construction method using mutually suitable Latin squares. For $$n \le 16$$ n ≤ 16 , we determine the maximum size among sets of mutually unbiased weighing matrices of order n and weight 9. Notably, our findings reveal that 13 is the smallest order where such pairs exist, and 16 is the first order for which a maximum class of unbiased weighing matrices is found.

We give new characterizations of the largest minimum weights among LCD codes of large dimensions. Using the characterizations, we completely determine the largest minimum weights among binary LCD codes of length n and dimension$n-6$, ternary LCD codes of length n and dimension$n-5$and quaternary Hermitian LCD codes of length n and dimension$n-4$for arbitrary n. We also determine the largest minimum weights among binary LCD codes of length n and dimension$n-7$, ternary LCD codes of length n and dimension$n-6$and quaternary Hermitian LCD codes of length n and dimension$n-5$with only some exceptions n.

The largest minimum weights among quaternary Hermitian linear complementary dual codes are known for dimension 2. In this paper, we give some conditions on the nonexistence of quaternary Hermitian linear complementary dual codes with large minimum weights. As a consequence, we completely determine the largest minimum weights for dimension 3, by using a classification of some quaternary codes. In addition, for a positive integer s, an entanglement-assisted quantum error-correcting [[21s + 5, 3, 16s + 3; 21s + 2]] code with maximal entanglement is constructed for the first time from a quaternary Hermitian linear complementary dual [26, 3, 19] code.