Information on Result #1439200
Linear OOA(5125, 15666, F5, 2, 24) (dual of [(15666, 2), 31207, 25]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5125, 15666, F5, 24) (dual of [15666, 15541, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5124, 15664, F5, 24) (dual of [15664, 15540, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5115, 15625, F5, 24) (dual of [15625, 15510, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(585, 15625, F5, 18) (dual of [15625, 15540, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5124, 15665, F5, 23) (dual of [15665, 15541, 24]-code), using Gilbert–Varšamov bound and bm = 5124 > Vbs−1(k−1) = 2 993348 063300 096959 819587 812452 609976 447525 017592 785631 333080 167981 902766 953551 235905 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(5124, 15664, F5, 24) (dual of [15664, 15540, 25]-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(5125, 7833, F5, 3, 24) (dual of [(7833, 3), 23374, 25]-NRT-code) | [i] | OOA Folding | |