In coding theory, the problem of finding shortest linear codes for a fixed set parameters is central. Given dimension $k$, minimum weight $d$, and order $q$ finite field $\bF_q$ over which code defined, function $n_q(k, d)$ specifies smallest length $n$ an $[n, k, d]_q$ exists. The determining values this known as optimal codes. Using geometric methods through projective geometry, we determine ...

A subspace of a finite extension field is called a Sidon space if the product of any two of its elements is unique up to a scalarmultiplier from the base field. Sidon spaces were recently introduced by Bachoc et al. as a means to characterize multiplicativeproperties of subspaces, and yet no explicit constructions were given. In this paper, several constructions of Sidon spaces arep...

The hulls of linear and cyclic codes have been extensively studied due to their wide applications. The dimensions and average dimension of the Euclidean hull of linear and cyclic codes have been well-studied. In this paper, the average dimension of the Hermitian hull of constacyclic codes of length n over a finite field Fq2 is determined together with some upper and lower bounds. It turns out t...