Fixed Hamming distance property of binary deletion correcting codes - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-20T06:31:50Z http://mathoverflow.net/feeds/question/64476 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/64476/fixed-hamming-distance-property-of-binary-deletion-correcting-codes Fixed Hamming distance property of binary deletion correcting codes Farzaneh 2011-05-10T07:35:49Z 2011-05-10T13:08:58Z <p>Let $x=(x_1x_2...x_n)$ be a binary sequence of length $n$. The Varshamov-Tenengolts code $VT_0(n)$ consists of all binary vectors $(x_1, . . . , x_n)$ satisfying $\Sigma_{i=1}^n i*x_i \equiv0 \pmod {n+1}$.</p> <p>Prove that $\forall$ $x,y \in VT_0(n)$ which has equal hamming weight the Hamming distance between $x$ and $y$ is exactly 4. For a binary vectore $x$ the hamming weight is $w$ if $\Sigma_{i=1}^n x_i= w$. </p> http://mathoverflow.net/questions/64476/fixed-hamming-distance-property-of-binary-deletion-correcting-codes/64496#64496 Answer by Gerry Myerson for Fixed Hamming distance property of binary deletion correcting codes Gerry Myerson 2011-05-10T13:08:58Z 2011-05-10T13:08:58Z <p>Take $n=11$. 11000000100 and 00111000000 are both in the code and they both have Hamming weight 3 but the Hamming distance between them is 6. </p>