Information on Result #2226535
Linear OA(2209, 530, F2, 48) (dual of [530, 321, 49]-code), using 1 times truncation based on linear OA(2210, 531, F2, 49) (dual of [531, 321, 50]-code), using
- construction XX applied to C1 = C([509,44]), C2 = C([0,46]), C3 = C1 + C2 = C([0,44]), and C∩ = C1 ∩ C2 = C([509,46]) [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 = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,46], and designed minimum distance d ≥ |I|+1 = 48 [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 = {−2,−1,…,46}, and designed minimum distance d ≥ |I|+1 = 50 [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(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
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code) (see above)
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(2231, 586, F2, 48) (dual of [586, 355, 49]-code) | [i] | Varšamov–Edel Lengthening | |
| 2 | Linear OA(2232, 592, F2, 48) (dual of [592, 360, 49]-code) | [i] | ||
| 3 | Linear OA(2233, 599, F2, 48) (dual of [599, 366, 49]-code) | [i] | ||
| 4 | Linear OA(2234, 606, F2, 48) (dual of [606, 372, 49]-code) | [i] | ||
| 5 | Linear OOA(2209, 265, F2, 2, 48) (dual of [(265, 2), 321, 49]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2209, 176, F2, 3, 48) (dual of [(176, 3), 319, 49]-NRT-code) | [i] | ||
| 7 | Linear OOA(2209, 132, F2, 4, 48) (dual of [(132, 4), 319, 49]-NRT-code) | [i] | ||
| 8 | Linear OOA(2209, 106, F2, 5, 48) (dual of [(106, 5), 321, 49]-NRT-code) | [i] | ||