Information on Result #672325
Linear OA(2249, 524308, F2, 27) (dual of [524308, 524059, 28]-code), using construction X applied to Ce(26) ⊂ Ce(24) based on
- linear OA(2248, 524288, F2, 27) (dual of [524288, 524040, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(2229, 524288, F2, 25) (dual of [524288, 524059, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(21, 20, F2, 1) (dual of [20, 19, 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 OA(2249, 524308, F2, 26) (dual of [524308, 524059, 27]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2250, 524309, F2, 27) (dual of [524309, 524059, 28]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2251, 524310, F2, 27) (dual of [524310, 524059, 28]-code) | [i] | ||
| 4 | Linear OA(2252, 524311, F2, 27) (dual of [524311, 524059, 28]-code) | [i] | ||
| 5 | Linear OA(2253, 524312, F2, 27) (dual of [524312, 524059, 28]-code) | [i] | ||
| 6 | Linear OA(2248, 524307, F2, 26) (dual of [524307, 524059, 27]-code) | [i] | Truncation | |
| 7 | Linear OOA(2249, 262154, F2, 2, 27) (dual of [(262154, 2), 524059, 28]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2249, 174769, F2, 3, 27) (dual of [(174769, 3), 524058, 28]-NRT-code) | [i] | ||
| 9 | Linear OOA(2249, 131077, F2, 4, 27) (dual of [(131077, 4), 524059, 28]-NRT-code) | [i] | ||
| 10 | Linear OOA(2249, 104861, F2, 5, 27) (dual of [(104861, 5), 524056, 28]-NRT-code) | [i] | ||
| 11 | Linear OOA(2249, 87384, F2, 6, 27) (dual of [(87384, 6), 524055, 28]-NRT-code) | [i] | ||
| 12 | Linear OOA(2249, 74901, F2, 7, 27) (dual of [(74901, 7), 524058, 28]-NRT-code) | [i] | ||
| 13 | Linear OOA(2249, 65538, F2, 8, 27) (dual of [(65538, 8), 524055, 28]-NRT-code) | [i] | ||
| 14 | Linear OOA(2249, 40331, F2, 27, 27) (dual of [(40331, 27), 1088688, 28]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |