Information on Result #682694
Linear OA(594, 15646, F5, 19) (dual of [15646, 15552, 20]-code), using construction X applied to Ce(18) ⊂ Ce(15) based on
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(53, 21, F5, 2) (dual of [21, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(53, 24, F5, 2) (dual of [24, 21, 3]-code), 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(595, 15647, F5, 19) (dual of [15647, 15552, 20]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(594, 11946, F5, 2, 19) (dual of [(11946, 2), 23798, 20]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 3 | Linear OOA(594, 11946, F5, 3, 19) (dual of [(11946, 3), 35744, 20]-NRT-code) | [i] | ||
| 4 | Digital (75, 94, 11946)-net over F5 | [i] | ||
| 5 | Linear OOA(594, 7823, F5, 2, 19) (dual of [(7823, 2), 15552, 20]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(594, 5215, F5, 3, 19) (dual of [(5215, 3), 15551, 20]-NRT-code) | [i] | ||
| 7 | Linear OOA(594, 1738, F5, 19, 19) (dual of [(1738, 19), 32928, 20]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |