Information on Result #672197
Linear OA(2250, 4194355, F2, 23) (dual of [4194355, 4194105, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
- linear OA(2243, 4194304, F2, 23) (dual of [4194304, 4194061, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2199, 4194304, F2, 19) (dual of [4194304, 4194105, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 222−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(2250, 4194355, F2, 22) (dual of [4194355, 4194105, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2251, 4194356, F2, 23) (dual of [4194356, 4194105, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2252, 4194357, F2, 23) (dual of [4194357, 4194105, 24]-code) | [i] | ||
| 4 | Linear OA(2253, 4194358, F2, 23) (dual of [4194358, 4194105, 24]-code) | [i] | ||
| 5 | Linear OA(2249, 4194354, F2, 22) (dual of [4194354, 4194105, 23]-code) | [i] | Truncation | |
| 6 | Linear OOA(2250, 2097177, F2, 2, 23) (dual of [(2097177, 2), 4194104, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2250, 1398118, F2, 3, 23) (dual of [(1398118, 3), 4194104, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2250, 1048588, F2, 4, 23) (dual of [(1048588, 4), 4194102, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2250, 838871, F2, 5, 23) (dual of [(838871, 5), 4194105, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2250, 699059, F2, 6, 23) (dual of [(699059, 6), 4194104, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2250, 599193, F2, 7, 23) (dual of [(599193, 7), 4194101, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2250, 524294, F2, 8, 23) (dual of [(524294, 8), 4194102, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2250, 381304, F2, 23, 23) (dual of [(381304, 23), 8769742, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |