The depth spectrums of constacyclic codes over finite chain rings

Abstract

a b s t r a c tIn light of the generator polynomials of constacyclic codes over finite chain rings, the depth spectrum of constacyclic codes can be determined if (n, p) = 1.

Quantum codes from constacyclic codes over $S_{k}$

“…Let C be a (2u 2 1 -1)-constacyclic code of length 3 over S 1 with generator polynomial e 1 g 1 (x) + e 2 g 2 (x) + e 3 g 3 (x), where g 1 = x + 3, g 2 = x + 5, g 3 = x + 4. By Theorem 8, we have C ⊥ ⊆ C, and φ 1 (C) is a linear code over F 7 with parameters [9,6,2]. By Theorem 9, we know that there is a quantum error correcting code with parameters [[9, 3, ≥ 2]] 7 .…”

“…Calderbank et al [1] gave a way to construct quantum error correcting codes from classical error correcting codes, constructing quantum error correcting codes is a systematic and effective mathematical method by using constacyclic codes. There are a lot of works about constacyclic codes over finite fields and finite rings [2][3][4][5][6][7][8][9][10] and many good quantum codes constructed by using cyclic codes over finite rings [11][12][13][14]. Currently, some authors have obtained quantum codes from constacyclic codes over finite non-chain ring.…”

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

“…The depth spectrum of cyclic codes over Z 4 of odd length was introduced by Zhu et al [5] . Later, the depth spectrum of simple-root constacyclic codes over a finite chain ring has been determined by Kong et al [6] . Recently, the depth spectrum of negacyclic codes over Z 4 of even length has been completely determined by Kai et al [7] .…”

Finite nonassociative algebras obtained from skew polynomials and possible applications to (<i>f</i>, <i>σ</i>, <i>δ</i>)-codes

“…We will look at the special case where S is a finite chain ring. Lately, these rings gained substantial momentum in coding theory, see for instance [3], [4], [7], [11], [14], [15], [27], [30]. A finite unital commutative ring R = {0} is called a finite chain ring, if its ideals are linearly ordered by inclusion.…”

“…We will look at the special case where S is a finite chain ring. Lately, these rings gained substantial momentum in coding theory, see for instance [3], [4], [7], [11], [14], [15], [27], [30].…”