Information on Result #708180
Linear OA(4117, 1050, F4, 30) (dual of [1050, 933, 31]-code), using construction XX applied to C1 = C([313,340]), C2 = C([317,342]), C3 = C1 + C2 = C([317,340]), and C∩ = C1 ∩ C2 = C([313,342]) based on
- linear OA(4105, 1023, F4, 28) (dual of [1023, 918, 29]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {313,314,…,340}, and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(496, 1023, F4, 26) (dual of [1023, 927, 27]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,342}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4111, 1023, F4, 30) (dual of [1023, 912, 31]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {313,314,…,342}, and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(490, 1023, F4, 24) (dual of [1023, 933, 25]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {317,318,…,340}, and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 7, F4, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-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(4117, 525, F4, 2, 30) (dual of [(525, 2), 933, 31]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4117, 350, F4, 3, 30) (dual of [(350, 3), 933, 31]-NRT-code) | [i] | ||