Information on Result #672297
Linear OA(262, 1048598, F2, 7) (dual of [1048598, 1048536, 8]-code), using construction X4 applied to Ce(6) ⊂ Ce(4) based on
- linear OA(261, 1048576, F2, 7) (dual of [1048576, 1048515, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(241, 1048576, F2, 5) (dual of [1048576, 1048535, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(221, 22, F2, 21) (dual of [22, 1, 22]-code or 22-arc in PG(20,2)), using
- dual of repetition code with length 22 [i]
- linear OA(21, 22, F2, 1) (dual of [22, 21, 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(262, 1048598, F2, 6) (dual of [1048598, 1048536, 7]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(263, 1048599, F2, 7) (dual of [1048599, 1048536, 8]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(261, 1048597, F2, 6) (dual of [1048597, 1048536, 7]-code) | [i] | Truncation | |
| 4 | Linear OOA(262, 524299, F2, 2, 7) (dual of [(524299, 2), 1048536, 8]-NRT-code) | [i] | OOA Folding | |