Information on Result #2225421
Linear OA(2143, 131113, F2, 16) (dual of [131113, 130970, 17]-code), using 1 times truncation based on linear OA(2144, 131114, F2, 17) (dual of [131114, 130970, 18]-code), using
- construction X applied to C([0,8]) ⊂ C([0,6]) [i] based on
- linear OA(2137, 131073, F2, 17) (dual of [131073, 130936, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(2103, 131073, F2, 13) (dual of [131073, 130970, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(27, 41, F2, 3) (dual of [41, 34, 4]-code or 41-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(2143, 65556, F2, 2, 16) (dual of [(65556, 2), 130969, 17]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(2143, 43704, F2, 3, 16) (dual of [(43704, 3), 130969, 17]-NRT-code) | [i] | ||
| 3 | Linear OOA(2143, 32778, F2, 4, 16) (dual of [(32778, 4), 130969, 17]-NRT-code) | [i] | ||
| 4 | Linear OOA(2143, 26222, F2, 5, 16) (dual of [(26222, 5), 130967, 17]-NRT-code) | [i] | ||
| 5 | Linear OOA(2143, 21852, F2, 6, 16) (dual of [(21852, 6), 130969, 17]-NRT-code) | [i] | ||
| 6 | Linear OOA(2143, 18730, F2, 7, 16) (dual of [(18730, 7), 130967, 17]-NRT-code) | [i] | ||
| 7 | Linear OOA(2143, 16389, F2, 8, 16) (dual of [(16389, 8), 130969, 17]-NRT-code) | [i] | ||
| 8 | Linear OOA(2143, 16389, F2, 16, 16) (dual of [(16389, 16), 262081, 17]-NRT-code) | [i] | OA Folding and Stacking | |