Information on Result #672649
Linear OA(2176, 16420, F2, 25) (dual of [16420, 16244, 26]-code), using construction X applied to C([0,12]) ⊂ C([0,10]) based on
- linear OA(2169, 16385, F2, 25) (dual of [16385, 16216, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2141, 16385, F2, 21) (dual of [16385, 16244, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385 | 228−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(27, 35, F2, 3) (dual of [35, 28, 4]-code or 35-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(2176, 16420, F2, 24) (dual of [16420, 16244, 25]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2177, 16421, F2, 25) (dual of [16421, 16244, 26]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2178, 16422, F2, 25) (dual of [16422, 16244, 26]-code) | [i] | ||
| 4 | Linear OA(2179, 16423, F2, 25) (dual of [16423, 16244, 26]-code) | [i] | ||
| 5 | Linear OA(2180, 16424, F2, 25) (dual of [16424, 16244, 26]-code) | [i] | ||
| 6 | Linear OA(2175, 16419, F2, 24) (dual of [16419, 16244, 25]-code) | [i] | Truncation | |
| 7 | Linear OOA(2176, 8210, F2, 2, 25) (dual of [(8210, 2), 16244, 26]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2176, 5473, F2, 3, 25) (dual of [(5473, 3), 16243, 26]-NRT-code) | [i] | ||
| 9 | Linear OOA(2176, 4105, F2, 4, 25) (dual of [(4105, 4), 16244, 26]-NRT-code) | [i] | ||
| 10 | Linear OOA(2176, 3284, F2, 5, 25) (dual of [(3284, 5), 16244, 26]-NRT-code) | [i] | ||