0
$\begingroup$

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} $.

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 $.

$\endgroup$
  • 1
    $\begingroup$ What exactly is the question? $\endgroup$ – Abel Stolz May 10 '11 at 8:52
3
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.