2026/07/22 by Yoonjin Lee, Junyong Park
Engineering · Computer Science · #graph theory and CDMA systems #Coding theory and cryptography #Advanced Wireless Communication Techniques
paper · doi:10.1080/03081087.2026.2681140
We study constructions of linear rank metric codes over finite fields Fq, focussing on the maximum rank distance (MRD) codes. Our constructions are based on the rank metric orbit codes under the actions of orthogonal groups over finite fields of odd characteristic. We consider three types of orthogonal groups as follows. First, we employ the orthogonal groups consisting of the permutation matrices of degree n; in particular, we use the orthogonal dihedral groups Dn for n≥3. Second, we make use of some orthogonal cyclic groups generated by the companion matrices of primitive polynomials over Fq. We lastly use the non-abelian orthogonal groups which are isomorphic to non-abelian groups of order 8: the quaternion group Q8 and the dihedral group D4. Using these methods, we obtain some infinite families of linear MRD codes over Fq; some families consist of constant weight (quasi-) MRD codes.