Information on Result #894524
Linear OOA(2258, 4194334, F2, 2, 20) (dual of [(4194334, 2), 8388410, 21]-NRT-code), using (u, u+v)-construction based on
- linear OOA(228, 33, F2, 2, 10) (dual of [(33, 2), 38, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(228, 66, F2, 10) (dual of [66, 38, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(228, 67, F2, 10) (dual of [67, 39, 11]-code), using
- 1 times truncation [i] based on linear OA(229, 68, F2, 11) (dual of [68, 39, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(228, 64, F2, 11) (dual of [64, 36, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(225, 64, F2, 9) (dual of [64, 39, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 4, F2, 1) (dual of [4, 3, 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
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- 1 times truncation [i] based on linear OA(229, 68, F2, 11) (dual of [68, 39, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(228, 67, F2, 10) (dual of [67, 39, 11]-code), using
- OOA 2-folding [i] based on linear OA(228, 66, F2, 10) (dual of [66, 38, 11]-code), using
- linear OOA(2230, 4194301, F2, 2, 20) (dual of [(4194301, 2), 8388372, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2230, 8388602, F2, 20) (dual of [8388602, 8388372, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- OOA 2-folding [i] based on linear OA(2230, 8388602, F2, 20) (dual of [8388602, 8388372, 21]-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m 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(2258, 2097167, F2, 4, 20) (dual of [(2097167, 4), 8388410, 21]-NRT-code) | [i] | OOA Folding | |