Information on Result #709240
Linear OA(4207, 1050, F4, 54) (dual of [1050, 843, 55]-code), using construction XX applied to C1 = C([289,340]), C2 = C([293,342]), C3 = C1 + C2 = C([293,340]), and C∩ = C1 ∩ C2 = C([289,342]) based on
- linear OA(4195, 1023, F4, 52) (dual of [1023, 828, 53]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {289,290,…,340}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(4186, 1023, F4, 50) (dual of [1023, 837, 51]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,342}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4201, 1023, F4, 54) (dual of [1023, 822, 55]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {289,290,…,342}, and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(4180, 1023, F4, 48) (dual of [1023, 843, 49]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {293,294,…,340}, and designed minimum distance d ≥ |I|+1 = 49 [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(4207, 525, F4, 2, 54) (dual of [(525, 2), 843, 55]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4207, 350, F4, 3, 54) (dual of [(350, 3), 843, 55]-NRT-code) | [i] | ||