A bound on lightweight sequences with application to definite decoding (Corresp.)

It is shown that the number
M
of binary-valued
n
-tuples having fractional weight
\delta
or less,
0 < \delta \leq \frac{1}{3}
, such that no two
n
-tuples agree in any
L
consecutive positions, is bounded by
2^{2LH(\delta)+1}
. A set of
n
-tuples is constructed to show that this bound is not likely to be improved upon by any significant factor. This bound is used to show that the ratio
d_{DD}/n_{DD}
of definite-decoding minimum distance to definite-decoding constraint length is lower bounded by
H^{-l}[\frac{1}{6} \cdot (1 - R)/ (1+R)]
as
n_{DD}
grows without bound.