Information on Result #672210
Linear OA(2218, 2097202, F2, 21) (dual of [2097202, 2096984, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2211, 2097153, F2, 21) (dual of [2097153, 2096942, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2169, 2097153, F2, 17) (dual of [2097153, 2096984, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 242−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 49, F2, 3) (dual of [49, 42, 4]-code or 49-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(2218, 2097202, F2, 20) (dual of [2097202, 2096984, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2219, 2097203, F2, 21) (dual of [2097203, 2096984, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2220, 2097204, F2, 21) (dual of [2097204, 2096984, 22]-code) | [i] | ||
| 4 | Linear OA(2217, 2097201, F2, 20) (dual of [2097201, 2096984, 21]-code) | [i] | Truncation | |
| 5 | Linear OOA(2218, 1048601, F2, 2, 21) (dual of [(1048601, 2), 2096984, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2218, 699067, F2, 3, 21) (dual of [(699067, 3), 2096983, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2218, 524300, F2, 4, 21) (dual of [(524300, 4), 2096982, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2218, 419440, F2, 5, 21) (dual of [(419440, 5), 2096982, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2218, 349533, F2, 6, 21) (dual of [(349533, 6), 2096980, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2218, 299600, F2, 7, 21) (dual of [(299600, 7), 2096982, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2218, 262150, F2, 8, 21) (dual of [(262150, 8), 2096982, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2218, 209720, F2, 21, 21) (dual of [(209720, 21), 4403902, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |