Information on Result #2257078
Linear OA(288, 2097177, F2, 9) (dual of [2097177, 2097089, 10]-code), using 2 times code embedding in larger space based on linear OA(286, 2097175, F2, 9) (dual of [2097175, 2097089, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(285, 2097152, F2, 9) (dual of [2097152, 2097067, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(264, 2097152, F2, 7) (dual of [2097152, 2097088, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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
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(288, 699059, F2, 3, 9) (dual of [(699059, 3), 2097089, 10]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(288, 524294, F2, 5, 9) (dual of [(524294, 5), 2621382, 10]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |
| 3 | Linear OOA(288, 524294, F2, 6, 9) (dual of [(524294, 6), 3145676, 10]-NRT-code) | [i] | ||
| 4 | Linear OOA(288, 524294, F2, 7, 9) (dual of [(524294, 7), 3669970, 10]-NRT-code) | [i] | ||
| 5 | Linear OOA(288, 524294, F2, 8, 9) (dual of [(524294, 8), 4194264, 10]-NRT-code) | [i] | ||