Information on Result #2175222
Linear OA(2246, 580, F2, 53) (dual of [580, 334, 54]-code), using adding a parity check bit based on linear OA(2245, 579, F2, 52) (dual of [579, 334, 53]-code), using
- construction X applied to C([1,52]) ⊂ C([1,40]) [i] based on
- linear OA(2216, 511, F2, 52) (dual of [511, 295, 53]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [i]
- linear OA(2171, 511, F2, 40) (dual of [511, 340, 41]-code), using 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(229, 68, F2, 11) (dual of [68, 39, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
- linear OA(228, 64, F2, 11) (dual of [64, 36, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(225, 64, F2, 9) (dual of [64, 39, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(21, 4, F2, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(8) [i] based on
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(2246, 580, F2, 52) (dual of [580, 334, 53]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2247, 581, F2, 53) (dual of [581, 334, 54]-code) | [i] | Code Embedding in Larger Space | |
| 3 | Linear OOA(2246, 290, F2, 2, 53) (dual of [(290, 2), 334, 54]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2246, 193, F2, 3, 53) (dual of [(193, 3), 333, 54]-NRT-code) | [i] | ||