New bounds on binary linear codes of dimension eight (Corresp.)

Dodunekov, S.M.; Helleseth, Tor; Manev, Nikolai L.; Ytrehus, Øyvind

doi:10.1109/tit.1987.1057363

Cited by 19 publications

(13 citation statements)

References 12 publications

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“…By Theorem 2.16, B1 = B2 = 0. Hence the columns of a generator matrix of C are projectively distinct and so must be precisely the 40 distinct points of PG (3,3). Hence C is the simplex code with the required weight enumerator.…”

Section: Determination Of N3(k D) For K _< 4 For All Dmentioning

confidence: 99%

“…However, Problem 2 is the more natural version of the optimal codes problem because the Griesmer bound provides an important lower bound on nq(k, d) which, for given values of q and k, is attained for all sufficiently large values of d. Thus, for given q and k, solving Problem 2 for all d (or solving Problem 1 for all n) becomes a finite one. For q = 2, n2(k, d) is known for k -< 7 and for all d (van Tilborg [18]), while for k = 8, the number of unresolved cases has been reduced to 34 (Dodunekov et al [3], Ytrehus and Helleseth [20]). …”

Section: Introductionmentioning

confidence: 99%

“…Then Cmay be shortened (cf. Definition 2.8) to a[20,3,13]-code, D say, containing a word of weight 20. By Corollary 2.7, the code D has A20 = 2 and A i = 0 for i > 15.…”

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confidence: 99%

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Optimal ternary linear codes

1992

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Let nq(k, d) denote the smallest value ofn for which there exists a linear In, k, d]-code over GF(q). An In, k, d]-code whose length is equal to nq(k, d) is called optimal. The problem of finding nq(k, d) has received much attention for the case q = 2. We generalize several results to the case of an arbitrary prime power q as well as introducing new results and a detailed methodology to enable the problem to be tackled over any finite fidd.In particular, we study the problem with q = 3 and determine n3(k, d) for all d when k -< 4, and n3(5, d) for all but 30 values of d.

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Section: Determination Of N3(k D) For K _< 4 For All Dmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal ternary linear codes

1992

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“…In [3] , Dodunekov and Encheva have used this residual code technique to prove the following useful theorem . (2) n the distance of which from C is m , then the matrix…”

Section: Introductionmentioning

confidence: 99%

“…If m ϭ 2 or 3 , then d ϭ 60 or 56 , and the result follows using Lemma 2 . 3 or [3] . If k Ͼ 10 and m ϭ 0 then , by Theorem 2 .…”

Section: Introductionmentioning

confidence: 99%