Repeated-root constacyclic codes of length \(kl^{a}p^{b}\) over a finite field. (English) Zbl 1372.94466
Summary: In this paper, we give an sufficient and necessary condition that a polynomial is irreducible over \(\mathbb{F}_q\). For different odd primes \(k\), \(l\) and \(p\), we obtain generator polynomials of constacyclic codes of length \(k l^a p^b\) over finite field \(\mathbb{F}_q\), where \(\text{char} \mathbb{F}_q = p\) and \((\text{ord}_k q, l) = 1\). And we answer the question in [B. Chen, Finite Fields Appl. 33, 137–159 (2015; Zbl 1368.11133)] under the condition.
MSC:
| 94B15 | Cyclic codes |
| 94B05 | Linear codes (general theory) |
| 11T71 | Algebraic coding theory; cryptography (number-theoretic aspects) |
Citations:
Zbl 1368.11133References:
| [1] | Bakshi, G. K., A class of constacyclic codes over a finite field, Finite Fields Appl., 18, 362-377 (2012) · Zbl 1250.94067 |
| [2] | Chen, B.; Dinh, H. Q.; Liu, H., Repeated-root constacyclic codes of length \(l p^s\) and their duals, Discrete Appl. Math., 177, 60-70 (2014) · Zbl 1325.94156 |
| [3] | Chen, B.; Dinh, H. Q.; Liu, H., Repeated-root constacyclic codes of length \(2 l^m p^n\), Finite Fields Appl., 33, 137-159 (2015) · Zbl 1368.11133 |
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| [8] | Dinh, H. Q., Structure of repeated-root cyclic and negacyclic codes of length \(6 p^s\) and their duals, AMS Contemp. Math., 609, 69-87 (2014) · Zbl 1321.94132 |
| [9] | Lidl, R.; Niederreiter, H., Finite Fields (2008), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1139.11053 |
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