Optimal quaternary linear codes of dimension five

Boukliev, I.; Daskalov, Rumen; Kapralov, Stoyan

doi:10.1109/18.508846

Cited by 10 publications

(3 citation statements)

References 6 publications

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“…It has been mentioned already that there is a (76,4)-cap in PG (3,5) constructed as a Griesmer code in [1]. Let us note that the only possible intersection numbers of this cap are 1, 6, 11, and 16.…”

Section: Caps With N =mentioning

confidence: 96%

“…Such a cap is associated with a [76, 4, 60] 5 -code which is divisible with weights 60,65,70,75. Actually the code from [1] does not have words of weight 75. Hence the multiplicities of the planes in a 76-solid are 16, 11, 6, and, possibly 1.…”

Section: Theorem 9 Letmentioning

confidence: 97%

“…For example, if we take q = 5, t = 3, n = 4, s = 2, we have m 4 (2, 5) = 16 and (2) is k ≤ 76. In fact, a [76, 4, 60] 5 -code has been constructed in [1], which is equivalent to a (76, 4)-cap in PG (3,5) meeting the upper bound.…”

Section: Corollarymentioning

confidence: 99%

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On multiple caps in finite projective spaces

Edel

Landjev

2010

Des. Codes Cryptogr.

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In this paper, we consider new results on (k, n)-caps with n > 2. We provide a lower bound on the size of such caps. Furthermore, we generalize two product constructions for (k, 2)-caps to caps with larger n. We give explicit constructions for good caps with small n. In particular, we determine the largest size of a (k, 3)-cap in PG(3, 5), which turns out to be 44. The results on caps in PG(3, 5) provide a solution to four of the eight open instances of the main coding theory problem for q = 5 and k = 4

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Section: Caps With N =mentioning

confidence: 96%

Section: Theorem 9 Letmentioning

confidence: 97%