Cyclic codes over local Frobenius rings of order 16

Skew constacyclic codes over the local Frobenius non-chain rings of order 16

“…We begin with the rings R 1 , R 2 and R 5 . 2 , where w = uv, was given as R 1 in [12]. Notice that this ring is a member of the family of rings R k studied in [17], [18], and [19].…”

“…Table 1 lists the optimal binary linear codes obtained from skew cyclic codes R 1 . h = x + uv + 1 [24,4,12] The codes in Table 2 have the parameters of best known linear codes in [32]. 24,16] In Table 3, we give information about the new binary QC codes obtained from skew cyclic codes R 1 according to [31] a "quaternary code" in this paper, we mean a code over Z 4 ) from codes over any of these 4 rings.…”

“…Codes over the local Frobenius non-chain rings were studied in [15] and [16] and a Gray map to the binary Hamming space was defined which applies to each of the rings in this family. Cyclic and constacyclic codes over these rings were studied in [12], and in [14] respectively, and relationship between cyclic and constacyclic codes was given. Numerous optimal binary codes were also obtained via the Gray map.…”

“…2 , uv , where w = u 2 , was given as R 2 in[12]. A non-trivial automorphism of R 2 is given as follows: θ 2 (a + bu + cv + dv 2 ) = a + cu + bv + dv 2 .…”

Constacyclic codes over F_q + u F_q + v F_q + u v F_q

“…Recently, other classes of rings which are non-chain rings have been introduced. Linear codes and some constacyclic codes over some local frobenius ring have been studied [7,12]. Most recently constacyclic codes over finite principal ideal ring have been investigated [2].…”