<s>
In	O
coding	B-Error_Name
theory	I-Error_Name
,	O
alternant	B-Error_Name
codes	I-Error_Name
form	O
a	O
class	O
of	O
parameterised	O
error-correcting	B-Error_Name
codes	I-Error_Name
which	O
generalise	O
the	O
BCH	O
codes	O
.	O
</s>
<s>
An	O
alternant	B-Error_Name
code	I-Error_Name
over	O
GF(q )	O
of	O
length	O
n	O
is	O
defined	O
by	O
a	O
parity	O
check	O
matrix	O
H	O
of	O
alternant	B-Algorithm
form	O
Hi	O
,	O
j	O
=	O
αjiyi	O
,	O
where	O
the	O
αj	O
are	O
distinct	O
elements	O
of	O
the	O
extension	O
GF(qm )	O
,	O
the	O
yi	O
are	O
further	O
non-zero	O
parameters	O
again	O
in	O
the	O
extension	O
GF(qm )	O
and	O
the	O
indices	O
range	O
as	O
i	O
from	O
0	O
to	O
δ1	O
,	O
j	O
from	O
1	O
to	O
n	O
.	O
</s>
<s>
The	O
parameters	O
of	O
this	O
alternant	B-Error_Name
code	I-Error_Name
are	O
length	O
n	O
,	O
dimension	O
≥	O
nmδ	O
and	O
minimum	O
distance	O
≥δ+1	O
.	O
</s>
<s>
There	O
exist	O
long	O
alternant	B-Error_Name
codes	I-Error_Name
which	O
meet	O
the	O
Gilbert	O
–	O
Varshamov	O
bound	O
.	O
</s>
