Information on Result #2223608
Linear OA(2116, 2076, F2, 20) (dual of [2076, 1960, 21]-code), using 1 times truncation based on linear OA(2117, 2077, F2, 21) (dual of [2077, 1960, 22]-code), using
- construction X applied to C([0,10]) ⊂ C([0,8]) [i] based on
- linear OA(2111, 2049, F2, 21) (dual of [2049, 1938, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(289, 2049, F2, 17) (dual of [2049, 1960, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2049 | 222−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(26, 28, F2, 3) (dual of [28, 22, 4]-code or 28-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), 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 OA(2118, 2078, F2, 20) (dual of [2078, 1960, 21]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2119, 2079, F2, 20) (dual of [2079, 1960, 21]-code) | [i] | ||
| 3 | Linear OOA(2116, 1038, F2, 2, 20) (dual of [(1038, 2), 1960, 21]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2116, 692, F2, 3, 20) (dual of [(692, 3), 1960, 21]-NRT-code) | [i] | ||
| 5 | Linear OOA(2116, 519, F2, 4, 20) (dual of [(519, 4), 1960, 21]-NRT-code) | [i] | ||
| 6 | Linear OOA(2116, 415, F2, 5, 20) (dual of [(415, 5), 1959, 21]-NRT-code) | [i] | ||
| 7 | Linear OOA(2116, 346, F2, 6, 20) (dual of [(346, 6), 1960, 21]-NRT-code) | [i] | ||
| 8 | Linear OOA(2116, 296, F2, 7, 20) (dual of [(296, 7), 1956, 21]-NRT-code) | [i] | ||
| 9 | Linear OOA(2116, 259, F2, 8, 20) (dual of [(259, 8), 1956, 21]-NRT-code) | [i] | ||