Information on Result #709229
Linear OA(4198, 1041, F4, 52) (dual of [1041, 843, 53]-code), using construction XX applied to C1 = C([1022,48]), C2 = C([1,50]), C3 = C1 + C2 = C([1,48]), and C∩ = C1 ∩ C2 = C([1022,50]) based on
- 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 = {−1,0,…,48}, and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4190, 1023, F4, 50) (dual of [1023, 833, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(4196, 1023, F4, 52) (dual of [1023, 827, 53]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,50}, and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(4180, 1023, F4, 48) (dual of [1023, 843, 49]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,48], and designed minimum distance d ≥ |I|+1 = 49 [i]
- 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
- linear OA(41, 11, F4, 1) (dual of [11, 10, 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 (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(4198, 520, F4, 2, 52) (dual of [(520, 2), 842, 53]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4198, 347, F4, 3, 52) (dual of [(347, 3), 843, 53]-NRT-code) | [i] | ||