Information on Result #836067
Linear OOA(5103, 195328, F5, 2, 16) (dual of [(195328, 2), 390553, 17]-NRT-code), using OOA 2-folding based on linear OA(5103, 390656, F5, 16) (dual of [390656, 390553, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(565, 390625, F5, 11) (dual of [390625, 390560, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(55, 30, F5, 3) (dual of [30, 25, 4]-code or 30-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
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
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 OOA(5103, 195328, F5, 3, 16) (dual of [(195328, 3), 585881, 17]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (87, 103, 195328)-net over F5 | [i] | ||