Information on Result #708110
Linear OA(4116, 1063, F4, 29) (dual of [1063, 947, 30]-code), using construction XX applied to C1 = C([1019,20]), C2 = C([0,24]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([1019,24]) based on
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,20}, and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(491, 1023, F4, 25) (dual of [1023, 932, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4106, 1023, F4, 29) (dual of [1023, 917, 30]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−4,−3,…,24}, and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(476, 1023, F4, 21) (dual of [1023, 947, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(45, 20, F4, 3) (dual of [20, 15, 4]-code or 20-cap in PG(4,4)) (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 OA(4115, 1062, F4, 28) (dual of [1062, 947, 29]-code) | [i] | Truncation | |
| 2 | Linear OOA(4116, 531, F4, 2, 29) (dual of [(531, 2), 946, 30]-NRT-code) | [i] | OOA Folding | |