Information on Result #861012
Linear OOA(2527, 314, F25, 2, 14) (dual of [(314, 2), 601, 15]-NRT-code), using OOA 2-folding based on linear OA(2527, 628, F25, 14) (dual of [628, 601, 15]-code), using
- construction XX applied to C1 = C([623,11]), C2 = C([0,12]), C3 = C1 + C2 = C([0,11]), and C∩ = C1 ∩ C2 = C([623,12]) [i] based on
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,11}, and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2525, 624, F25, 13) (dual of [624, 599, 14]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(2527, 624, F25, 14) (dual of [624, 597, 15]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,12}, and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [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(2534, 340, F25, 2, 14) (dual of [(340, 2), 646, 15]-NRT-code) | [i] | (u, u+v)-Construction for OOAs | |
| 2 | Linear OOA(2535, 341, F25, 2, 14) (dual of [(341, 2), 647, 15]-NRT-code) | [i] | ||
| 3 | Linear OOA(2536, 342, F25, 2, 14) (dual of [(342, 2), 648, 15]-NRT-code) | [i] | ||
| 4 | Linear OOA(2537, 366, F25, 2, 14) (dual of [(366, 2), 695, 15]-NRT-code) | [i] | ||
| 5 | Linear OOA(2538, 380, F25, 2, 14) (dual of [(380, 2), 722, 15]-NRT-code) | [i] | ||
| 6 | Digital (13, 27, 303)-net over F25 | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |