Information on Result #673374
Linear OA(2233, 573, F2, 51) (dual of [573, 340, 52]-code), using construction X applied to Ce(50) ⊂ Ce(40) based on
- linear OA(2208, 512, F2, 51) (dual of [512, 304, 52]-code), using an extension Ce(50) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
- linear OA(2172, 512, F2, 41) (dual of [512, 340, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [i]
- linear OA(225, 61, F2, 9) (dual of [61, 36, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(225, 63, F2, 9) (dual of [63, 38, 10]-code), 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(2233, 573, F2, 50) (dual of [573, 340, 51]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2234, 574, F2, 51) (dual of [574, 340, 52]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OA(2235, 575, F2, 51) (dual of [575, 340, 52]-code) | [i] | ||
| 4 | Linear OA(2236, 576, F2, 51) (dual of [576, 340, 52]-code) | [i] | ||
| 5 | Linear OA(2232, 572, F2, 50) (dual of [572, 340, 51]-code) | [i] | Truncation | |
| 6 | Linear OOA(2233, 286, F2, 2, 51) (dual of [(286, 2), 339, 52]-NRT-code) | [i] | OOA Folding | |
| 7 | Linear OOA(2233, 191, F2, 3, 51) (dual of [(191, 3), 340, 52]-NRT-code) | [i] | ||