Main results in the paper are obtained by computation over Magma V2.26-10. We show all of our computation programs and log files.
(EV) OS: macOS Monterey 12.0.1, at 2.6 GHz CPU 6 Core (Intel Core i7) and 16GB memory.

• Codes and log files: Enumeration.zip, and Automorphism.zip (uploaded at May 29th, 2022)

  1. In the folder "Enumeration", there are two kinds of codes for enumerating s.sp. curves. We here describe the case of q=23:

     • "SSpHyper_g4_F23.txt" (txt)

Code for listing s.sp. hyperelliptic curves of genus 4 over F23 (without isomorphism classification).

• 1. • "Isom_SSpHyper_g4_F23.txt" (txt)

Code for computing representatives of all F23-isomorphism and \overline{F23}-isomorphism classes of the s.sp. curves listed by the above code.

• 2. In the folder "Automorphism", there are two kinds of codes for enumerating s.sp. curves. We here describe the case of q=23:

     • "Aut_SSpHyper_g4_F23.txt" (txt)

Code for computing automorphism groups over F23 and over \overline{F23} of each isomorphism class of s.sp. curves over F23. Sigma-conjugacy groups and sigma-stabilizers are also computed.

• 2. • "Aut_SSpHyper_g4_F23_magma.txt" (txt)

Code for computing automorphism groups over F23 and over \overline{F23} of each isomorphism class of s.sp. curves over F23. Different from the file "Aut_SSpHyper_g4_F23.txt", this code adopts Magma's built-in functions "AutomorphismGroupOfHyperellipticCurve" and "GeometricAutomorphismGroup".

The zip file also contains log files which are are named "result_mac_*code name*.txt.