Information on Result #712367
Linear OA(5147, 657, F5, 44) (dual of [657, 510, 45]-code), using construction XX applied to C1 = C([621,36]), C2 = C([1,40]), C3 = C1 + C2 = C([1,36]), and C∩ = C1 ∩ C2 = C([621,40]) based on
- linear OA(5127, 624, F5, 40) (dual of [624, 497, 41]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−3,−2,…,36}, and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(5126, 624, F5, 40) (dual of [624, 498, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(5139, 624, F5, 44) (dual of [624, 485, 45]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−3,−2,…,40}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(5114, 624, F5, 36) (dual of [624, 510, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(54, 17, F5, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,5)), using
- linear OA(54, 16, F5, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,5)), using
- discarding factors / shortening the dual code based on linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)) (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(5147, 219, F5, 3, 44) (dual of [(219, 3), 510, 45]-NRT-code) | [i] | OOA Folding | |