Information on Result #1549041
Linear OOA(5107, 15662, F5, 3, 21) (dual of [(15662, 3), 46879, 22]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OA(5107, 15662, F5, 21) (dual of [15662, 15555, 22]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5103, 15655, F5, 21) (dual of [15655, 15552, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(597, 15625, F5, 21) (dual of [15625, 15528, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(573, 15625, F5, 16) (dual of [15625, 15552, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(56, 30, F5, 4) (dual of [30, 24, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5103, 15658, F5, 19) (dual of [15658, 15555, 20]-code), using Gilbert–Varšamov bound and bm = 5103 > Vbs−1(k−1) = 33991 648155 809588 076181 086724 730334 880932 325183 587962 436298 912740 804325 [i]
- linear OA(51, 4, F5, 1) (dual of [4, 3, 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(5103, 15655, F5, 21) (dual of [15655, 15552, 22]-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(5107, 3915, F5, 27, 21) (dual of [(3915, 27), 105598, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |