Information on Result #2174951
Linear OA(2109, 1062, F2, 21) (dual of [1062, 953, 22]-code), using adding a parity check bit based on linear OA(2108, 1061, F2, 20) (dual of [1061, 953, 21]-code), using
- construction XX applied to C1 = C([1019,14]), C2 = C([1,16]), C3 = C1 + C2 = C([1,14]), and C∩ = C1 ∩ C2 = C([1019,16]) [i] based on
- linear OA(291, 1023, F2, 19) (dual of [1023, 932, 20]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,14}, and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(280, 1023, F2, 16) (dual of [1023, 943, 17]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2101, 1023, F2, 21) (dual of [1023, 922, 22]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−4,−3,…,16}, and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(270, 1023, F2, 14) (dual of [1023, 953, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(26, 27, F2, 3) (dual of [27, 21, 4]-code or 27-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
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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
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(2109, 1062, F2, 20) (dual of [1062, 953, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2110, 1063, F2, 21) (dual of [1063, 953, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2109, 531, F2, 2, 21) (dual of [(531, 2), 953, 22]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2109, 354, F2, 3, 21) (dual of [(354, 3), 953, 22]-NRT-code) | [i] | ||
| 5 | Linear OOA(2109, 177, F2, 6, 21) (dual of [(177, 6), 953, 22]-NRT-code) | [i] | ||