Information on Result #702724
Linear OA(253, 1046, F2, 10) (dual of [1046, 993, 11]-code), using construction XX applied to C1 = C([1021,6]), C2 = C([1,8]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C([1021,8]) based on
- linear OA(241, 1023, F2, 9) (dual of [1023, 982, 10]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(240, 1023, F2, 8) (dual of [1023, 983, 9]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(251, 1023, F2, 11) (dual of [1023, 972, 12]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−2,−1,…,8}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(230, 1023, F2, 6) (dual of [1023, 993, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 12, F2, 1) (dual of [12, 11, 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), 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 (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(254, 1047, F2, 11) (dual of [1047, 993, 12]-code) | [i] | Adding a Parity Check Bit | |
| 2 | Linear OOA(253, 523, F2, 2, 10) (dual of [(523, 2), 993, 11]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(253, 209, F2, 5, 10) (dual of [(209, 5), 992, 11]-NRT-code) | [i] | ||
| 4 | Linear OOA(253, 209, F2, 6, 10) (dual of [(209, 6), 1201, 11]-NRT-code) | [i] | OA Folding and Stacking | |
| 5 | Linear OOA(253, 209, F2, 7, 10) (dual of [(209, 7), 1410, 11]-NRT-code) | [i] | ||
| 6 | Linear OOA(253, 209, F2, 8, 10) (dual of [(209, 8), 1619, 11]-NRT-code) | [i] | ||
| 7 | Linear OOA(253, 209, F2, 10, 10) (dual of [(209, 10), 2037, 11]-NRT-code) | [i] | ||