Information on Result #1314514
Linear OA(2578, 776, F25, 36) (dual of [776, 698, 37]-code), using 138 step Varšamov–Edel lengthening with (ri) = (5, 0, 1, 4 times 0, 1, 11 times 0, 1, 22 times 0, 1, 38 times 0, 1, 56 times 0) based on linear OA(2568, 628, F25, 36) (dual of [628, 560, 37]-code), using
- construction XX applied to C1 = C([623,33]), C2 = C([0,34]), C3 = C1 + C2 = C([0,33]), and C∩ = C1 ∩ C2 = C([623,34]) [i] based on
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,33}, and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2566, 624, F25, 35) (dual of [624, 558, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(2568, 624, F25, 36) (dual of [624, 556, 37]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,34}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2564, 624, F25, 34) (dual of [624, 560, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [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(2578, 776, F25, 2, 36) (dual of [(776, 2), 1474, 37]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Digital (42, 78, 776)-net over F25 | [i] | ||
| 3 | Linear OOA(2578, 388, F25, 2, 36) (dual of [(388, 2), 698, 37]-NRT-code) | [i] | OOA Folding | |