Information on Result #711252
Linear OA(561, 632, F5, 19) (dual of [632, 571, 20]-code), using construction XX applied to C1 = C([623,16]), C2 = C([0,17]), C3 = C1 + C2 = C([0,16]), and C∩ = C1 ∩ C2 = C([623,17]) based on
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,16}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(557, 624, F5, 18) (dual of [624, 567, 19]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(561, 624, F5, 19) (dual of [624, 563, 20]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−1,0,…,17}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(553, 624, F5, 17) (dual of [624, 571, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [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 OA(564, 649, F5, 19) (dual of [649, 585, 20]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(565, 673, F5, 19) (dual of [673, 608, 20]-code) | [i] | ||
| 3 | Linear OA(566, 713, F5, 19) (dual of [713, 647, 20]-code) | [i] | ||
| 4 | Linear OA(567, 769, F5, 19) (dual of [769, 702, 20]-code) | [i] | ||
| 5 | Linear OA(568, 836, F5, 19) (dual of [836, 768, 20]-code) | [i] | ||
| 6 | Linear OA(569, 912, F5, 19) (dual of [912, 843, 20]-code) | [i] | ||
| 7 | Linear OOA(561, 316, F5, 2, 19) (dual of [(316, 2), 571, 20]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(561, 210, F5, 3, 19) (dual of [(210, 3), 569, 20]-NRT-code) | [i] | ||