Information on Result #1700070
Linear OOA(2167, 209724, F2, 8, 16) (dual of [(209724, 8), 1677625, 17]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2167, 209724, F2, 5, 16) (dual of [(209724, 5), 1048453, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2167, 1048620, F2, 16) (dual of [1048620, 1048453, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2167, 1048623, F2, 16) (dual of [1048623, 1048456, 17]-code), using
- 1 times truncation [i] based on linear OA(2168, 1048624, F2, 17) (dual of [1048624, 1048456, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2161, 1048577, F2, 17) (dual of [1048577, 1048416, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2121, 1048577, F2, 13) (dual of [1048577, 1048456, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-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
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- 1 times truncation [i] based on linear OA(2168, 1048624, F2, 17) (dual of [1048624, 1048456, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2167, 1048623, F2, 16) (dual of [1048623, 1048456, 17]-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 | Linear OOA(2167, 209723, F2, 24, 16) (dual of [(209723, 24), 5033185, 17]-NRT-code) | [i] | OOA Stacking with Additional Row | |