Information on Result #860774
Linear OOA(2513, 314, F25, 2, 7) (dual of [(314, 2), 615, 8]-NRT-code), using OOA 2-folding based on linear OA(2513, 628, F25, 7) (dual of [628, 615, 8]-code), using
- construction XX applied to C1 = C([623,4]), C2 = C([0,5]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([623,5]) [i] based on
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,4}, and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2511, 624, F25, 6) (dual of [624, 613, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(2513, 624, F25, 7) (dual of [624, 611, 8]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(259, 624, F25, 5) (dual of [624, 615, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
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(2516, 340, F25, 2, 7) (dual of [(340, 2), 664, 8]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2517, 628, F25, 2, 7) (dual of [(628, 2), 1239, 8]-NRT-code) | [i] | ||
| 3 | Linear OOA(2579, 4194615, F25, 2, 14) (dual of [(4194615, 2), 8389151, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2584, 4194615, F25, 2, 15) (dual of [(4194615, 2), 8389146, 16]-NRT-code) | [i] | ||
| 5 | Digital (6, 13, 314)-net over F25 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |