By Topic

Some new results on the minimum length of binary linear codes of dimension nine

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
Dodunekov, S. ; Inst. of Math. & Inf., Bulgarian Acad. of Sci., Sofia, Bulgaria ; Guritman, S. ; Simonis, J.

Let n(k, d) be the smallest integer n for which a binary linear code of length n, dimension k, and minimum distance d exists. Using the residual code technique, the MacWilliams identities and the weight distribution of appropriate Reed-Muller codes, we prove that n(9, 64)=133, n(9, 120)⩾244, n(9, 124)=252, and n(9, 184)=371. We also show that puncturing a known [322, 9, 160]-code yields length-optimal codes with parameters [319, 9, 158], [315, 9, 156], and [312, 9, 154]

Published in:

Information Theory, IEEE Transactions on  (Volume:45 ,  Issue: 7 )