Information on Result #672160
Linear OA(2228, 4194356, F2, 21) (dual of [4194356, 4194128, 22]-code), using construction X applied to C([0,10]) ⊂ C([0,8]) based on
- linear OA(2221, 4194305, F2, 21) (dual of [4194305, 4194084, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 244−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(2177, 4194305, F2, 17) (dual of [4194305, 4194128, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 244−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(27, 51, F2, 3) (dual of [51, 44, 4]-code or 51-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(2228, 4194356, F2, 20) (dual of [4194356, 4194128, 21]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2229, 4194357, F2, 21) (dual of [4194357, 4194128, 22]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2230, 4194358, F2, 21) (dual of [4194358, 4194128, 22]-code) | [i] | ||
| 4 | Linear OA(2227, 4194355, F2, 20) (dual of [4194355, 4194128, 21]-code) | [i] | Truncation | |
| 5 | Linear OOA(2228, 2097178, F2, 2, 21) (dual of [(2097178, 2), 4194128, 22]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(2228, 1398118, F2, 3, 21) (dual of [(1398118, 3), 4194126, 22]-NRT-code) | [i] | ||
| 7 | Linear OOA(2228, 1048589, F2, 4, 21) (dual of [(1048589, 4), 4194128, 22]-NRT-code) | [i] | ||
| 8 | Linear OOA(2228, 838871, F2, 5, 21) (dual of [(838871, 5), 4194127, 22]-NRT-code) | [i] | ||
| 9 | Linear OOA(2228, 699059, F2, 6, 21) (dual of [(699059, 6), 4194126, 22]-NRT-code) | [i] | ||
| 10 | Linear OOA(2228, 599193, F2, 7, 21) (dual of [(599193, 7), 4194123, 22]-NRT-code) | [i] | ||
| 11 | Linear OOA(2228, 524294, F2, 8, 21) (dual of [(524294, 8), 4194124, 22]-NRT-code) | [i] | ||
| 12 | Linear OOA(2228, 419435, F2, 21, 21) (dual of [(419435, 21), 8807907, 22]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |