Parameters of two classes of negacyclic BCH codes

• Published in: Journal of applied mathematics & computing Vol. 69; no. 6; pp. 4353 - 4380
• Main Authors: Zhu, Huilian, Li, Jin, Zhu, Shixin
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2023; Springer Nature B.V
• Subjects: BCH codes; Computational Mathematics and Numerical Analysis; Lower bounds; Mathematical and Computational Engineering; Mathematics; Mathematics and Statistics; Mathematics of Computing; Original Research; Parameters; Theory of Computation; 94B15; BCH code; Negacyclic BCH code; Negacyclic code; Cyclotomic coset; 94B05
• ISSN: 1598-5865; 1865-2085
• DOI: 10.1007/s12190-023-01929-w

Negacyclic BCH codes are a generalization of BCH codes, they have better parameters than BCH codes in some cases. In this paper, we investigate negacyclic BCH codes of length
q
m
+
1
2
and
q
m
-
1
2
λ
over
F
q
, where
q
≥
3
is an odd prime power and
λ
is an integer with
2
≤
λ
≤
q
-
1
,
λ
∣
(
q
-
1
)
and
2
λ
∣
(
q
m
-
1
)
. By using some results on the
q
-cyclotomic cosets modulo
q
m
+
1
or
q
m
-
1
λ
, we determine the dimensions of these two classes of negacyclic BCH codes, and give some lower bounds on the minimum distance of these codes.