Information on Result #672302
Linear OA(2228, 1048623, F2, 23) (dual of [1048623, 1048395, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
- linear OA(2221, 1048576, F2, 23) (dual of [1048576, 1048355, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2181, 1048576, F2, 19) (dual of [1048576, 1048395, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(27, 47, F2, 3) (dual of [47, 40, 4]-code or 47-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, 1048623, F2, 22) (dual of [1048623, 1048395, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2229, 1048624, F2, 23) (dual of [1048624, 1048395, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2230, 1048625, F2, 23) (dual of [1048625, 1048395, 24]-code) | [i] | ||
| 4 | Linear OA(2231, 1048626, F2, 23) (dual of [1048626, 1048395, 24]-code) | [i] | ||
| 5 | Linear OA(2227, 1048622, F2, 22) (dual of [1048622, 1048395, 23]-code) | [i] | Truncation | |
| 6 | Linear OOA(2228, 524311, F2, 2, 23) (dual of [(524311, 2), 1048394, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2228, 349541, F2, 3, 23) (dual of [(349541, 3), 1048395, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2228, 262155, F2, 4, 23) (dual of [(262155, 4), 1048392, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2228, 209724, F2, 5, 23) (dual of [(209724, 5), 1048392, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2228, 174770, F2, 6, 23) (dual of [(174770, 6), 1048392, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2228, 149803, F2, 7, 23) (dual of [(149803, 7), 1048393, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2228, 131077, F2, 8, 23) (dual of [(131077, 8), 1048388, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2228, 95329, F2, 23, 23) (dual of [(95329, 23), 2192339, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |