Information on Result #1692656
Linear OOA(259, 7034, F2, 8, 8) (dual of [(7034, 8), 56213, 9]-NRT-code), using appending kth column based on linear OOA(259, 7034, F2, 7, 8) (dual of [(7034, 7), 49179, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(259, 7034, F2, 2, 8) (dual of [(7034, 2), 14009, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(259, 8200, F2, 2, 8) (dual of [(8200, 2), 16341, 9]-NRT-code), using
- 21 times duplication [i] based on linear OOA(258, 8200, F2, 2, 8) (dual of [(8200, 2), 16342, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(258, 16400, F2, 8) (dual of [16400, 16342, 9]-code), using
- strength reduction [i] based on linear OA(258, 16400, F2, 9) (dual of [16400, 16342, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(257, 16384, F2, 9) (dual of [16384, 16327, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(243, 16384, F2, 7) (dual of [16384, 16341, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 16383 = 214−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(215, 16, F2, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,2)), using
- dual of repetition code with length 16 [i]
- linear OA(21, 16, F2, 1) (dual of [16, 15, 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 X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- strength reduction [i] based on linear OA(258, 16400, F2, 9) (dual of [16400, 16342, 10]-code), using
- OOA 2-folding [i] based on linear OA(258, 16400, F2, 8) (dual of [16400, 16342, 9]-code), using
- 21 times duplication [i] based on linear OOA(258, 8200, F2, 2, 8) (dual of [(8200, 2), 16342, 9]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(259, 8200, F2, 2, 8) (dual of [(8200, 2), 16341, 9]-NRT-code), using
Mode: 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 | Digital (51, 59, 7034)-net over F2 | [i] | Net Defined by OOA | |