The concatenated structure of cyclic and Abelian codes

Factoring ofx n?1 and orthogonalization over finite fields of characteristic 2

“…This yields a new procedure which is easy to understand. Moreover our method fits in with the description of cyclic codes over extensions of GF(2) and can be used for obtaining abelian codes as concatenations of cyclic codes [4,6].…”

“…Our interest in this problem comes from [6] where it is shown that abelian codes over a finite field can be obtained by taking concatenations of cyclic codes over extensions of this field. Thus in order to construct binary abelian codes by this method, we must know how to factor x" 1 over GF(2 s) I-4].…”

Artin–Schreier curves and weights of two-dimensional cyclic codes

“…It is important to note that an analogue of the representations in (12) and (13) can also be obtained vertically. For this, we look at the columns of v g in (10). The first column is ðx i g Þ xAA ; the second column is ða j g x i g Þ xAA ; etc.…”

“…There is another lower bound on the minimum distance of 2-D cyclic codes due to Jensen (see [10,11]). He utilizes the concatenated structure of 2-D cyclic codes to come up with this bound.…”

Codes From Symmetry Groups, and a $[32, 17, 8]$ Code

“…Representation theory has also been used to construct codes by Liebler [23], Camion [12], Rabizzoni [32], Ward [34], Zlotnik [36], Klemm [21], Charpin [13], [14], Bhattacharya [6], Jensen [20], Wolfmann [35], and Landrock and Manz [22].…”