Information on Result #672355
Linear OA(2217, 524333, F2, 23) (dual of [524333, 524116, 24]-code), using construction X applied to Ce(22) ⊂ Ce(18) based on
- linear OA(2210, 524288, F2, 23) (dual of [524288, 524078, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(2172, 524288, F2, 19) (dual of [524288, 524116, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 524287 = 219−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [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(2217, 524333, F2, 22) (dual of [524333, 524116, 23]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2218, 524334, F2, 23) (dual of [524334, 524116, 24]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2219, 524335, F2, 23) (dual of [524335, 524116, 24]-code) | [i] | ||
| 4 | Linear OA(2220, 524336, F2, 23) (dual of [524336, 524116, 24]-code) | [i] | ||
| 5 | Linear OA(2216, 524332, F2, 22) (dual of [524332, 524116, 23]-code) | [i] | Truncation | |
| 6 | Linear OOA(2217, 262166, F2, 2, 23) (dual of [(262166, 2), 524115, 24]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2217, 174777, F2, 3, 23) (dual of [(174777, 3), 524114, 24]-NRT-code) | [i] | ||
| 8 | Linear OOA(2217, 131083, F2, 4, 23) (dual of [(131083, 4), 524115, 24]-NRT-code) | [i] | ||
| 9 | Linear OOA(2217, 104866, F2, 5, 23) (dual of [(104866, 5), 524113, 24]-NRT-code) | [i] | ||
| 10 | Linear OOA(2217, 87388, F2, 6, 23) (dual of [(87388, 6), 524111, 24]-NRT-code) | [i] | ||
| 11 | Linear OOA(2217, 74904, F2, 7, 23) (dual of [(74904, 7), 524111, 24]-NRT-code) | [i] | ||
| 12 | Linear OOA(2217, 65541, F2, 8, 23) (dual of [(65541, 8), 524111, 24]-NRT-code) | [i] | ||
| 13 | Linear OOA(2217, 47666, F2, 23, 23) (dual of [(47666, 23), 1096101, 24]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |