Information on Result #672315
Linear OA(2198, 524334, F2, 21) (dual of [524334, 524136, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2191, 524289, F2, 21) (dual of [524289, 524098, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2153, 524289, F2, 17) (dual of [524289, 524136, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 524289 | 238−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 45, F2, 3) (dual of [45, 38, 4]-code or 45-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(2198, 524334, F2, 20) (dual of [524334, 524136, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2199, 524335, F2, 21) (dual of [524335, 524136, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2200, 524336, F2, 21) (dual of [524336, 524136, 22]-code) | [i] | ||
| 4 | Linear OA(2197, 524333, F2, 20) (dual of [524333, 524136, 21]-code) | [i] | Truncation | |
| 5 | Linear OOA(2198, 262167, F2, 2, 21) (dual of [(262167, 2), 524136, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2198, 174778, F2, 3, 21) (dual of [(174778, 3), 524136, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2198, 131083, F2, 4, 21) (dual of [(131083, 4), 524134, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2198, 104866, F2, 5, 21) (dual of [(104866, 5), 524132, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2198, 87389, F2, 6, 21) (dual of [(87389, 6), 524136, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2198, 74904, F2, 7, 21) (dual of [(74904, 7), 524130, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2198, 65541, F2, 8, 21) (dual of [(65541, 8), 524130, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2198, 52433, F2, 21, 21) (dual of [(52433, 21), 1100895, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |