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

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

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:

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