Information on Result #682670
Linear OA(586, 15638, F5, 18) (dual of [15638, 15552, 19]-code), using construction X applied to Ce(17) ⊂ Ce(15) based on
- 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(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(51, 13, F5, 1) (dual of [13, 12, 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
Mode: Constructive and 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 OA(587, 15639, F5, 18) (dual of [15639, 15552, 19]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(586, 8774, F5, 2, 18) (dual of [(8774, 2), 17462, 19]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(586, 8774, F5, 3, 18) (dual of [(8774, 3), 26236, 19]-NRT-code) | [i] | ||
| 4 | Digital (68, 86, 8774)-net over F5 | [i] | ||
| 5 | Linear OOA(586, 7819, F5, 2, 18) (dual of [(7819, 2), 15552, 19]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(586, 5212, F5, 3, 18) (dual of [(5212, 3), 15550, 19]-NRT-code) | [i] | ||
| 7 | Linear OOA(586, 1737, F5, 18, 18) (dual of [(1737, 18), 31180, 19]-NRT-code) | [i] | OA Folding and Stacking | |