Information on Result #702399
Linear OA(2165, 532, F2, 38) (dual of [532, 367, 39]-code), using construction XX applied to C1 = C([509,34]), C2 = C([1,36]), C3 = C1 + C2 = C([1,34]), and C∩ = C1 ∩ C2 = C([509,36]) based on
- linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,34}, and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(2153, 511, F2, 36) (dual of [511, 358, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(2144, 511, F2, 34) (dual of [511, 367, 35]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- 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
- 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 (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(2170, 537, F2, 38) (dual of [537, 367, 39]-code) | [i] | Code Embedding in Larger Space | |
| 2 | Linear OA(2171, 538, F2, 38) (dual of [538, 367, 39]-code) | [i] | ||
| 3 | Linear OA(2166, 533, F2, 39) (dual of [533, 367, 40]-code) | [i] | Adding a Parity Check Bit | |
| 4 | Linear OOA(2165, 266, F2, 2, 38) (dual of [(266, 2), 367, 39]-NRT-code) | [i] | OOA Folding | |
| 5 | Linear OOA(2165, 177, F2, 3, 38) (dual of [(177, 3), 366, 39]-NRT-code) | [i] | ||
| 6 | Linear OOA(2165, 133, F2, 4, 38) (dual of [(133, 4), 367, 39]-NRT-code) | [i] | ||