Information on Result #1531354
Linear OOA(3231, 29560, F3, 3, 32) (dual of [(29560, 3), 88449, 33]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(3231, 29560, F3, 2, 32) (dual of [(29560, 2), 58889, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3231, 59120, F3, 32) (dual of [59120, 58889, 33]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(3226, 59114, F3, 32) (dual of [59114, 58888, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3211, 59049, F3, 32) (dual of [59049, 58838, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(3161, 59049, F3, 25) (dual of [59049, 58888, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(315, 65, F3, 6) (dual of [65, 50, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- construction X applied to Ce(31) ⊂ Ce(24) [i] based on
- linear OA(3226, 59115, F3, 27) (dual of [59115, 58889, 28]-code), using Gilbert–Varšamov bound and bm = 3226 > Vbs−1(k−1) = 1917 862275 617060 586840 663518 725615 888366 338598 140496 768996 758472 955172 027472 597059 535343 125552 349869 895721 [i]
- linear OA(34, 5, F3, 4) (dual of [5, 1, 5]-code or 5-arc in PG(3,3)), using
- dual of repetition code with length 5 [i]
- linear OA(3226, 59114, F3, 32) (dual of [59114, 58888, 33]-code), using
- construction X with Varšamov bound [i] based on
Mode: Linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(3231, 14780, F3, 5, 32) (dual of [(14780, 5), 73669, 33]-NRT-code) | [i] | OOA Folding | |