Information on Result #708336
Linear OA(4122, 1039, F4, 32) (dual of [1039, 917, 33]-code), using construction XX applied to C1 = C([1021,28]), C2 = C([0,29]), C3 = C1 + C2 = C([0,28]), and C∩ = C1 ∩ C2 = C([1021,29]) based on
- linear OA(4116, 1023, F4, 31) (dual of [1023, 907, 32]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,28}, and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(4111, 1023, F4, 30) (dual of [1023, 912, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4121, 1023, F4, 32) (dual of [1023, 902, 33]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−2,−1,…,29}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(4106, 1023, F4, 29) (dual of [1023, 917, 30]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,28], and designed minimum distance d ≥ |I|+1 = 30 [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(4122, 1039, F4, 2, 32) (dual of [(1039, 2), 1956, 33]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(4122, 1039, F4, 3, 32) (dual of [(1039, 3), 2995, 33]-NRT-code) | [i] | ||
| 3 | Digital (90, 122, 1039)-net over F4 | [i] | ||
| 4 | Linear OA(4123, 1054, F4, 32) (dual of [1054, 931, 33]-code) | [i] | Varšamov–Edel Lengthening | |
| 5 | Linear OA(4124, 1084, F4, 32) (dual of [1084, 960, 33]-code) | [i] | ||
| 6 | Linear OOA(4122, 519, F4, 2, 32) (dual of [(519, 2), 916, 33]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(4122, 346, F4, 3, 32) (dual of [(346, 3), 916, 33]-NRT-code) | [i] | ||