Properties of m-sequence are derived, based on the properties, a family of binary nonlinear constant weight codes is presented, these binary nonlinear constant weight codes can be employed in automatic repeat request (ARQ) communication system. In addition, let Qq (n,d) denote the maximal possible number of codewords in any q-ary equidistant code of length n and Hamming distance d between codewords (with no restriction on weight), let Eq (n,d,w) denote the largest possible number of codewords in any q-ary equidistant code with constant weight, length n, constant weight w, Hamming distance d between codewords. Let q, n, d, w isin N, here N denotes natural number set. We show that 1) Eq (n,d,w) les qn, 2) Qq (n,d) les qn+1, when q > 2, and if q=2, then 3) Eq (n,d,w) les n, 4) Qq (n,d) les n+1
[1]
O. Antoine,et al.
Theory of Error-correcting Codes
,
2022
.
[2]
N. J. A. Sloane,et al.
A new table of constant weight codes
,
1990,
IEEE Trans. Inf. Theory.
[3]
Solomon W. Golomb,et al.
Shift Register Sequences
,
1981
.
[4]
Kellyann Geurts,et al.
A theory of error
,
2005,
C&C '05.
[5]
Richard W. Hamming,et al.
Coding and Information Theory
,
2018,
Feynman Lectures on Computation.
[6]
Jacobus H. van Lint,et al.
Introduction to Coding Theory
,
1982
.
[7]
Hu Chuan-Gan,et al.
On The Shift Register Sequences
,
2004
.