Information on Result #2226614
Linear OA(2214, 544, F2, 48) (dual of [544, 330, 49]-code), using 1 times truncation based on linear OA(2215, 545, F2, 49) (dual of [545, 330, 50]-code), using
- construction XX applied to C1 = C([507,42]), C2 = C([0,44]), C3 = C1 + C2 = C([0,42]), and C∩ = C1 ∩ C2 = C([507,44]) [i] based on
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,44], and designed minimum distance d ≥ |I|+1 = 46 [i]
- linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [i]
- linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
- linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-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, 10, F2, 1) (dual of [10, 9, 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(2230, 581, F2, 48) (dual of [581, 351, 49]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OOA(2214, 272, F2, 2, 48) (dual of [(272, 2), 330, 49]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2214, 181, F2, 3, 48) (dual of [(181, 3), 329, 49]-NRT-code) | [i] | ||
| 4 | Linear OOA(2214, 136, F2, 4, 48) (dual of [(136, 4), 330, 49]-NRT-code) | [i] | ||
| 5 | Linear OOA(2214, 108, F2, 5, 48) (dual of [(108, 5), 326, 49]-NRT-code) | [i] | ||