Multidimensional quasi-twisted codes: equivalent characterizations and their relation to multidimensional convolutional codes

Every Fq -linear code is equivalent to a non-trivial multi-twisted code

“…Then C is a [7,3,4] By Proposition 3.3, C ′′ = (2 + x 2 , 2 + x, 0), (1, 1 + x 2 , 1), (2 + x, x + 2x 2 , 0) as an…”

“…to C with the following generator matrix 4), and C ′′ = C ′(3,id,3,id,id,(1,2) (3,4)) is an equivalent code to C ′ with the following generator matrix Also C ′′ = C ′(id,id,4,id,id,id,id,id,(1,2)(3,4) (5,6)) is an equivalent code to C ′ with the following generator matrix…”

“…Cyclic and constacyclic linear codes have been generalized in various forms. Quasi-cyclic (QC) codes, quasi-twisted (QT) codes, generalized quasi-cyclic (GQC) codes, multi-twisted (MT) codes are important generalizations among cyclic and constacyclic codes which have attracted many researchers; see [14], [3,4,8], [2,6,13] and [1,10] respectively.…”

Every $ \mathbb{F}_q $-linear code is equivalent to a multi-twisted code

“…To prove part (6), let C be a λ-constacyclic code of length n with gcd(ord(λ (6), C is equivalent to a λ t -constacyclic code. We have λ t = 1 which completes the proof of (6).…”

“…These codes have been generalized in various forms. Quasi-cyclic (QC) codes, quasi-twisted (QT) codes, generalized quasi-cyclic (GQC) codes, Multitwisted (MT) codes in the linear case are important generalizations of cyclic and constacyclic codes which have attracted many researchers; see [4], [5,6,10], [2,8,3] and [1,12] respectively.…”