Constructions of optimal cyclic subspace codes via Sidon spaces

Let [Formula: see text] be the finite field with cardinality [Formula: see text], and let [Formula: see text] be positive integers, where [Formula: see text] is a factor of [Formula: see text]. Denote by [Formula: see text] the set of all [Formula: see text]-dimensional [Formula: see text]-subspaces of [Formula: see text]. Let [Formula: see text] be a positive integer and [Formula: see text] with [Formula: see text] and [Formula: see text] for any [Formula: see text]. If [Formula: see text], Zhang and Cao [Further constructions of cyclic subspace codes, Cryptogr. Commun. 13 (2021) 245–262] used the set [Formula: see text] to construct several cyclic subspace codes in [Formula: see text] with size [Formula: see text] and optimal minimum distance [Formula: see text]. Under the condition [Formula: see text], Niu, Xiao and Gao [Adv. Math. Commun. 18(4) (2024) 1123–1437] designed a kind of optimal cyclic subspace codes in [Formula: see text] with size [Formula: see text]. This paper further improves their results by using [Formula: see text] and variants of Sidon spaces in [Formula: see text]. In particular, when [Formula: see text] and [Formula: see text] is an odd prime, our code size can attain at [Formula: see text]. With the same parameters, this new code has optimal minimum distance [Formula: see text] and has more codewords than previous works.