Information on Result #708645
Linear OA(4168, 1070, F4, 42) (dual of [1070, 902, 43]-code), using construction XX applied to C1 = C([1018,32]), C2 = C([0,36]), C3 = C1 + C2 = C([0,32]), and C∩ = C1 ∩ C2 = C([1018,36]) based on
- linear OA(4141, 1023, F4, 38) (dual of [1023, 882, 39]-code), using the primitive BCH-code C(I) with length 1023 = 45−1, defining interval I = {−5,−4,…,32}, and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(4136, 1023, F4, 37) (dual of [1023, 887, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- 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 = {−5,−4,…,36}, and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(4121, 1023, F4, 33) (dual of [1023, 902, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(47, 27, F4, 4) (dual of [27, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- 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
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(4169, 1071, F4, 42) (dual of [1071, 902, 43]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OOA(4168, 535, F4, 2, 42) (dual of [(535, 2), 902, 43]-NRT-code) | [i] | OOA Folding | |