Information on Result #2258314
Linear OA(2165, 1048601, F2, 17) (dual of [1048601, 1048436, 18]-code), using 3 times code embedding in larger space based on linear OA(2162, 1048598, F2, 17) (dual of [1048598, 1048436, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2161, 1048576, F2, 17) (dual of [1048576, 1048415, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2141, 1048576, F2, 15) (dual of [1048576, 1048435, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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 OOA(2165, 131075, F2, 17, 17) (dual of [(131075, 17), 2228110, 18]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |