Information on Result #674042
Linear OA(2133, 159, F2, 55) (dual of [159, 26, 56]-code), using construction XX applied to Ce(54) ⊂ Ce(46) ⊂ Ce(42) based on
- linear OA(2113, 128, F2, 55) (dual of [128, 15, 56]-code), using an extension Ce(54) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [i]
- linear OA(2106, 128, F2, 47) (dual of [128, 22, 48]-code), using an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- linear OA(299, 128, F2, 43) (dual of [128, 29, 44]-code), using an extension Ce(42) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
- linear OA(212, 23, F2, 7) (dual of [23, 11, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- extended Golay code Ge(2) [i]
- discarding factors / shortening the dual code based on linear OA(212, 24, F2, 7) (dual of [24, 12, 8]-code), using
- linear OA(24, 8, F2, 3) (dual of [8, 4, 4]-code or 8-cap in PG(3,2)), 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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OA(2133, 159, F2, 54) (dual of [159, 26, 55]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2132, 158, F2, 54) (dual of [158, 26, 55]-code) | [i] | Truncation | |
| 3 | Linear OOA(2133, 79, F2, 2, 55) (dual of [(79, 2), 25, 56]-NRT-code) | [i] | OOA Folding | |
| 4 | Linear OOA(2133, 53, F2, 3, 55) (dual of [(53, 3), 26, 56]-NRT-code) | [i] | ||