Information on Result #712346
Linear OA(5135, 644, F5, 42) (dual of [644, 509, 43]-code), using construction XX applied to C1 = C([116,156]), C2 = C([120,157]), C3 = C1 + C2 = C([120,156]), and C∩ = C1 ∩ C2 = C([116,157]) based on
- linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,156}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,157}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(5131, 624, F5, 42) (dual of [624, 493, 43]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {116,117,…,157}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(5115, 624, F5, 37) (dual of [624, 509, 38]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {120,121,…,156}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- 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
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(5135, 322, F5, 2, 42) (dual of [(322, 2), 509, 43]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(5135, 214, F5, 3, 42) (dual of [(214, 3), 507, 43]-NRT-code) | [i] | ||