Information on Result #708542
Linear OA(4171, 1082, F4, 41) (dual of [1082, 911, 42]-code), using construction XX applied to C1 = C([305,340]), C2 = C([312,345]), C3 = C1 + C2 = C([312,340]), and C∩ = C1 ∩ C2 = C([305,345]) based on
- linear OA(4135, 1023, F4, 36) (dual of [1023, 888, 37]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {305,306,…,340}, and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(4126, 1023, F4, 34) (dual of [1023, 897, 35]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {312,313,…,345}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(4151, 1023, F4, 41) (dual of [1023, 872, 42]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {305,306,…,345}, and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4110, 1023, F4, 29) (dual of [1023, 913, 30]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {312,313,…,340}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(413, 36, F4, 6) (dual of [36, 23, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- linear OA(47, 23, F4, 4) (dual of [23, 16, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), 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(4171, 541, F4, 2, 41) (dual of [(541, 2), 911, 42]-NRT-code) | [i] | OOA Folding | |