Information on Result #1314564
Linear OA(2586, 695, F25, 41) (dual of [695, 609, 42]-code), using 59 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 0, 1, 7 times 0, 1, 15 times 0, 1, 30 times 0) based on linear OA(2578, 628, F25, 41) (dual of [628, 550, 42]-code), using
- construction XX applied to C1 = C([623,38]), C2 = C([0,39]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([623,39]) [i] based on
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,38}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2576, 624, F25, 40) (dual of [624, 548, 41]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,39], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(2578, 624, F25, 41) (dual of [624, 546, 42]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,39}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(2574, 624, F25, 39) (dual of [624, 550, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [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(2586, 695, F25, 2, 41) (dual of [(695, 2), 1304, 42]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (45, 86, 695)-net over F25 | [i] | ||
| 3 | Linear OOA(2586, 347, F25, 2, 41) (dual of [(347, 2), 608, 42]-NRT-code) | [i] | OOA Folding | |