Information on Result #1314463
Linear OA(2563, 708, F25, 29) (dual of [708, 645, 30]-code), using 71 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 9 times 0, 1, 18 times 0, 1, 34 times 0) based on linear OA(2554, 628, F25, 29) (dual of [628, 574, 30]-code), using
- construction XX applied to C1 = C([623,26]), C2 = C([0,27]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([623,27]) [i] based on
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,26}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2552, 624, F25, 28) (dual of [624, 572, 29]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(2554, 624, F25, 29) (dual of [624, 570, 30]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,27}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(2550, 624, F25, 27) (dual of [624, 574, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [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: 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(2563, 708, F25, 2, 29) (dual of [(708, 2), 1353, 30]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (34, 63, 708)-net over F25 | [i] | ||
| 3 | Linear OOA(2563, 354, F25, 2, 29) (dual of [(354, 2), 645, 30]-NRT-code) | [i] | OOA Folding | |