Information on Result #2258750
Linear OA(2200, 524336, F2, 21) (dual of [524336, 524136, 22]-code), using 2 times code embedding in larger space based on linear OA(2198, 524334, F2, 21) (dual of [524334, 524136, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2191, 524289, F2, 21) (dual of [524289, 524098, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2200, 131084, F2, 4, 21) (dual of [(131084, 4), 524136, 22]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2200, 65542, F2, 8, 21) (dual of [(65542, 8), 524136, 22]-NRT-code) | [i] | ||