Information on Result #1439014
Linear OOA(5121, 78163, F5, 2, 20) (dual of [(78163, 2), 156205, 21]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5121, 78163, F5, 20) (dual of [78163, 78042, 21]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5118, 78158, F5, 20) (dual of [78158, 78040, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(55, 33, F5, 3) (dual of [33, 28, 4]-code or 33-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5118, 78160, F5, 18) (dual of [78160, 78042, 19]-code), using Gilbert–Varšamov bound and bm = 5118 > Vbs−1(k−1) = 7 309069 901290 073384 883047 833310 024926 645612 110152 243656 144992 535681 611005 159565 [i]
- linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(5118, 78158, F5, 20) (dual of [78158, 78040, 21]-code), using
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(5121, 39081, F5, 3, 20) (dual of [(39081, 3), 117122, 21]-NRT-code) | [i] | OOA Folding | |