Information on Result #708865
Linear OA(4167, 1039, F4, 44) (dual of [1039, 872, 45]-code), using construction XX applied to C1 = C([1021,40]), C2 = C([0,41]), C3 = C1 + C2 = C([0,40]), and C∩ = C1 ∩ C2 = C([1021,41]) based on
- linear OA(4161, 1023, F4, 43) (dual of [1023, 862, 44]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,40}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(4156, 1023, F4, 42) (dual of [1023, 867, 43]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,41], 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 = {−2,−1,…,41}, and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
- 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, using
- linear OA(40, 5, F4, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-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(4167, 519, F4, 2, 44) (dual of [(519, 2), 871, 45]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4167, 346, F4, 3, 44) (dual of [(346, 3), 871, 45]-NRT-code) | [i] | ||