Information on Result #672492
Linear OA(2232, 65576, F2, 29) (dual of [65576, 65344, 30]-code), using construction X applied to C([0,14]) ⊂ C([0,12]) based on
- linear OA(2225, 65537, F2, 29) (dual of [65537, 65312, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-cap in PG(6,2)), using
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 4 [i]
- discarding factors / shortening the dual code based on linear OA(27, 63, F2, 3) (dual of [63, 56, 4]-code or 63-cap in PG(6,2)), 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(2232, 65576, F2, 28) (dual of [65576, 65344, 29]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2233, 65577, F2, 29) (dual of [65577, 65344, 30]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2234, 65578, F2, 29) (dual of [65578, 65344, 30]-code) | [i] | ||
| 4 | Linear OA(2235, 65579, F2, 29) (dual of [65579, 65344, 30]-code) | [i] | ||
| 5 | Linear OA(2236, 65580, F2, 29) (dual of [65580, 65344, 30]-code) | [i] | ||
| 6 | Linear OA(2231, 65575, F2, 28) (dual of [65575, 65344, 29]-code) | [i] | Truncation | |
| 7 | Linear OOA(2232, 32788, F2, 2, 29) (dual of [(32788, 2), 65344, 30]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2232, 21858, F2, 3, 29) (dual of [(21858, 3), 65342, 30]-NRT-code) | [i] | ||
| 9 | Linear OOA(2232, 16394, F2, 4, 29) (dual of [(16394, 4), 65344, 30]-NRT-code) | [i] | ||
| 10 | Linear OOA(2232, 13115, F2, 5, 29) (dual of [(13115, 5), 65343, 30]-NRT-code) | [i] | ||
| 11 | Linear OOA(2232, 10929, F2, 6, 29) (dual of [(10929, 6), 65342, 30]-NRT-code) | [i] | ||
| 12 | Linear OOA(2232, 9368, F2, 7, 29) (dual of [(9368, 7), 65344, 30]-NRT-code) | [i] | ||
| 13 | Linear OOA(2232, 8197, F2, 8, 29) (dual of [(8197, 8), 65344, 30]-NRT-code) | [i] | ||