Information on Result #1301674
Linear OA(5104, 15658, F5, 20) (dual of [15658, 15554, 21]-code), using construction X with Varšamov bound based on
- linear OA(5102, 15654, F5, 20) (dual of [15654, 15552, 21]-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(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-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(5102, 15656, F5, 19) (dual of [15656, 15554, 20]-code), using Gilbert–Varšamov bound and bm = 5102 > Vbs−1(k−1) = 33913 535144 688648 156537 961687 293412 555337 358822 851281 556968 524059 797165 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 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
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(5104, 15658, F5, 2, 20) (dual of [(15658, 2), 31212, 21]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5104, 15658, F5, 3, 20) (dual of [(15658, 3), 46870, 21]-NRT-code) | [i] | ||
| 3 | Digital (84, 104, 15658)-net over F5 | [i] | ||
| 4 | Linear OOA(5104, 7829, F5, 2, 20) (dual of [(7829, 2), 15554, 21]-NRT-code) | [i] | OOA Folding | |