Information on Result #702923
Linear OA(2229, 1095, F2, 42) (dual of [1095, 866, 43]-code), using construction XX applied to C1 = C([1017,30]), C2 = C([0,36]), C3 = C1 + C2 = C([0,30]), and C∩ = C1 ∩ C2 = C([1017,36]) based on
- linear OA(2181, 1023, F2, 37) (dual of [1023, 842, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−6,−5,…,30}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2206, 1023, F2, 43) (dual of [1023, 817, 44]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−6,−5,…,36}, and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(212, 36, F2, 5) (dual of [36, 24, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- linear OA(211, 32, F2, 5) (dual of [32, 21, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(4) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(212, 38, F2, 5) (dual of [38, 26, 6]-code), using
- linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(211, 44, F2, 4) (dual of [44, 33, 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 OA(2230, 1096, F2, 43) (dual of [1096, 866, 44]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(2229, 547, F2, 2, 42) (dual of [(547, 2), 865, 43]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2229, 365, F2, 3, 42) (dual of [(365, 3), 866, 43]-NRT-code) | [i] | ||
| 4 | Linear OOA(2229, 273, F2, 4, 42) (dual of [(273, 4), 863, 43]-NRT-code) | [i] | ||
| 5 | Linear OOA(2229, 219, F2, 5, 42) (dual of [(219, 5), 866, 43]-NRT-code) | [i] | ||
| 6 | Linear OOA(2229, 182, F2, 6, 42) (dual of [(182, 6), 863, 43]-NRT-code) | [i] | ||