Information on Result #672544
Linear OA(2248, 65575, F2, 31) (dual of [65575, 65327, 32]-code), using construction X applied to Ce(30) ⊂ Ce(26) based on
- linear OA(2241, 65536, F2, 31) (dual of [65536, 65295, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2209, 65536, F2, 27) (dual of [65536, 65327, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 216−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(27, 39, F2, 3) (dual of [39, 32, 4]-code or 39-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(2248, 65575, F2, 30) (dual of [65575, 65327, 31]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2249, 65576, F2, 31) (dual of [65576, 65327, 32]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2250, 65577, F2, 31) (dual of [65577, 65327, 32]-code) | [i] | ||
| 4 | Linear OA(2251, 65578, F2, 31) (dual of [65578, 65327, 32]-code) | [i] | ||
| 5 | Linear OA(2252, 65579, F2, 31) (dual of [65579, 65327, 32]-code) | [i] | ||
| 6 | Linear OA(2247, 65574, F2, 30) (dual of [65574, 65327, 31]-code) | [i] | Truncation | |
| 7 | Linear OOA(2248, 32787, F2, 2, 31) (dual of [(32787, 2), 65326, 32]-NRT-code) | [i] | OOA Folding | |
| 8 | Linear OOA(2248, 21858, F2, 3, 31) (dual of [(21858, 3), 65326, 32]-NRT-code) | [i] | ||
| 9 | Linear OOA(2248, 16393, F2, 4, 31) (dual of [(16393, 4), 65324, 32]-NRT-code) | [i] | ||
| 10 | Linear OOA(2248, 13115, F2, 5, 31) (dual of [(13115, 5), 65327, 32]-NRT-code) | [i] | ||
| 11 | Linear OOA(2248, 10929, F2, 6, 31) (dual of [(10929, 6), 65326, 32]-NRT-code) | [i] | ||
| 12 | Linear OOA(2248, 9367, F2, 7, 31) (dual of [(9367, 7), 65321, 32]-NRT-code) | [i] | ||