Year: 2025
Type: article
Abstract: We introduce homothetic-BCH codes. These are a family of $$q^2$$ q 2 -ary classical codes $$\mathcal {C}$$ C of length $$\lambda n_1$$ λ n 1 , where $$\lambda $$ λ and $$n_1$$ n 1 are suitable positive integers such that the punctured code $$\mathcal {B}$$ B of $$\mathcal {C}$$ C in the last $$\lambda n_1 -n_1$$ λ n 1 - n 1 coordinates is a narrow-sense BCH code of length $$n_1$$ n 1 . We prove that whenever $$\mathcal {B}$$ B is Hermitian self-orthogonal, so is $$\mathcal {C}$$ C . As a consequence, we present a procedure to obtain quantum stabilizer codes with lengths that cannot be reached by BCH codes. With this procedure, we get new quantum codes according to Grassl’s table (Grassl 2025). To prove our results, we give necessary and sufficient conditions for Hermitian self-orthogonality of BCH codes of a wide range of lengths.
Authors: C. Galindo, F. Hernando, H. Martín-Cruz
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,390
OpenAlex ID: W4417450570