Information on Result #673421
Linear OA(2224, 550, F2, 51) (dual of [550, 326, 52]-code), using construction XX applied to Ce(50) ⊂ Ce(44) ⊂ Ce(42) 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(2190, 512, F2, 45) (dual of [512, 322, 46]-code), using an extension Ce(44) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
- linear OA(2181, 512, F2, 43) (dual of [512, 331, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(211, 33, F2, 5) (dual of [33, 22, 6]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33 | 210−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(21, 5, F2, 1) (dual of [5, 4, 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
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(2223, 549, F2, 50) (dual of [549, 326, 51]-code) | [i] | Truncation | |
| 2 | Linear OOA(2224, 275, F2, 2, 51) (dual of [(275, 2), 326, 52]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2224, 183, F2, 3, 51) (dual of [(183, 3), 325, 52]-NRT-code) | [i] | ||
| 4 | Linear OOA(2224, 110, F2, 5, 51) (dual of [(110, 5), 326, 52]-NRT-code) | [i] | ||