Skew Cyclic Codes over a Non‐chain Ring

On the Depth Distribution of Constacyclic Codes over ℤ 4 of Length 2 e

“…The available values of (a 2 e −τ −i , a 3m−τ −i ) in Eq. (19) are (1, 0), (1, 2), (0, 1) and (0, 3), then there are 4 choices for (a 2 e −τ −i , a 3m−τ −i ) in Eq. (19).…”

“…(19) are (1, 0), (1, 2), (0, 1) and (0, 3), then there are 4 choices for (a 2 e −τ −i , a 3m−τ −i ) in Eq. (19). In addition, for each 2 e − i < j ≤ s − 1, there are 2 choices for a j−τ , and the available values of a j−τ are 0 and 1.…”

LCD Codes over 𝔽 q + v𝔽 q + v2𝔽 q + ⋯ + v m -1𝔽 q

“…The above quotation from Massey shows that in the beginning the motivation to investigate the linear codes with a complementary dual or linear complementary dual code (LCD codes for short) is purely algebraic in general [3][4][5][6]. However, since the last five years the LCD codes become a very active research area since their application to cryptography, in particular to protect an information against so-called "side-channel attacks (SCA)" or "fault non-invasive attacks", as shown by Carlet and Guilley [7].…”

Skew-Constacyclic Codes Over

“…In [14], Dertli et al explored skew-constacyclic and skew-quasi constacyclic codes over Z 3 [v]/ v 3 − v . Recently, Shi et al, in [22], studied skew cyclic codes over F p s [v]/ v m − v , where p is a prime and m − 1 divides p − 1. The motivation for studying this ring is lying under the facts that first this ring is as a natural generalization of codes over the ring F p [v]/ v p −v .…”

“…It is easy to see that any complete set of idempotents in R q is a basis of F q -vector space. Therefore, any element r of R q can be represented as: [22]. For i = 0, 1, • • • , q − 1, we consider the map…”