Information on Result #708876
Linear OA(4168, 1041, F4, 44) (dual of [1041, 873, 45]-code), using construction XX applied to C1 = C([1022,40]), C2 = C([1,42]), C3 = C1 + C2 = C([1,40]), and C∩ = C1 ∩ C2 = C([1022,42]) based on
- linear OA(4156, 1023, F4, 42) (dual of [1023, 867, 43]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,40}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4160, 1023, F4, 42) (dual of [1023, 863, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4166, 1023, F4, 44) (dual of [1023, 857, 45]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−1,0,…,42}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4150, 1023, F4, 40) (dual of [1023, 873, 41]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(4168, 520, F4, 2, 44) (dual of [(520, 2), 872, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4168, 347, F4, 3, 44) (dual of [(347, 3), 873, 45]-NRT-code) | [i] | ||