Information on Result #708826
Linear OA(4173, 1053, F4, 45) (dual of [1053, 880, 46]-code), using construction XX applied to C1 = C([1019,37]), C2 = C([0,40]), C3 = C1 + C2 = C([0,37]), and C∩ = C1 ∩ C2 = C([1019,40]) 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 = {−4,−3,…,37}, and designed minimum distance d ≥ |I|+1 = 43 [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(4166, 1023, F4, 45) (dual of [1023, 857, 46]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,40}, and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(4141, 1023, F4, 38) (dual of [1023, 882, 39]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,37], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(44, 17, F4, 3) (dual of [17, 13, 4]-code or 17-cap in PG(3,4)), using
- linear OA(43, 13, F4, 2) (dual of [13, 10, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-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(4173, 526, F4, 2, 45) (dual of [(526, 2), 879, 46]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(4173, 351, F4, 3, 45) (dual of [(351, 3), 880, 46]-NRT-code) | [i] | ||