Information on Result #702713
Linear OA(233, 1045, F2, 7) (dual of [1045, 1012, 8]-code), using construction XX applied to C1 = C([1021,2]), C2 = C([0,4]), C3 = C1 + C2 = C([0,2]), and C∩ = C1 ∩ C2 = C([1021,4]) based on
- linear OA(221, 1023, F2, 5) (dual of [1023, 1002, 6]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(221, 1023, F2, 5) (dual of [1023, 1002, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(231, 1023, F2, 7) (dual of [1023, 992, 8]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(211, 1023, F2, 3) (dual of [1023, 1012, 4]-code or 1023-cap in PG(10,2)), using the primitive expurgated narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code) (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(232, 1044, F2, 6) (dual of [1044, 1012, 7]-code) | [i] | Truncation | |
| 2 | Linear OOA(233, 522, F2, 2, 7) (dual of [(522, 2), 1011, 8]-NRT-code) | [i] | OOA Folding | |