Abstract
The binary Melas code is a cyclic code with generator polynomial
g
(
u
)=
p
(
u
)
p
(
u
)
∗
where
p
(
u
) is a primitive polynomial of odd degree
m
≥5 and the ∗ denotes reciprocation. The even-weight subcode of a Melas code has generator polynomial (
u
+1)
g
(
u
) and parameters [2
m
−1,2
m
−2
m
−2,6]. This code is lifted to
ℤ
4
and the quaternary code is shown to have parameters [2
m
−1,2
m
−2
m
−2,
d
L
≥8], where
d
L
denotes the minimum Lee distance. An algebraic decoding algorithm correcting all errors of Lee weight ≤3 is presented for this code. The Gray map of this quaternary code is a binary code with parameters [2
m
+1
−2,2
m
+1
−4
m
−4,
d
H
≥8] where
d
H
is the minimum Hamming distance. For
m
=5,7 the minimum distance equals the minimum distance of the best known linear code for the given length and code size.