Information on Result #712073
Linear OA(5107, 632, F5, 34) (dual of [632, 525, 35]-code), using construction XX applied to C1 = C([623,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([623,32]) based on
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(5103, 624, F5, 33) (dual of [624, 521, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(599, 624, F5, 32) (dual of [624, 525, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(50, 4, F5, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(50, 4, F5, 0) (dual of [4, 4, 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(5107, 632, F5, 2, 34) (dual of [(632, 2), 1157, 35]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(5107, 632, F5, 3, 34) (dual of [(632, 3), 1789, 35]-NRT-code) | [i] | ||
| 3 | Digital (73, 107, 632)-net over F5 | [i] | ||
| 4 | Linear OA(5108, 656, F5, 34) (dual of [656, 548, 35]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(5109, 687, F5, 34) (dual of [687, 578, 35]-code) | [i] | ||
| 6 | Linear OOA(5107, 316, F5, 2, 34) (dual of [(316, 2), 525, 35]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(5107, 210, F5, 3, 34) (dual of [(210, 3), 523, 35]-NRT-code) | [i] | ||