Information on Result #700629
Linear OA(290, 143, F2, 29) (dual of [143, 53, 30]-code), using construction XX applied to C1 = C({0,1,3,5,7,9,11,13,15,19,21,63}), C2 = C([0,23]), C3 = C1 + C2 = C([0,21]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,19,21,23,63}) based on
- linear OA(278, 127, F2, 25) (dual of [127, 49, 26]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,63}, and minimum distance d ≥ |{−2,−1,…,22}|+1 = 26 (BCH-bound) [i]
- linear OA(278, 127, F2, 27) (dual of [127, 49, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(285, 127, F2, 29) (dual of [127, 42, 30]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,19,21,23,63}, and minimum distance d ≥ |{−2,−1,…,26}|+1 = 30 (BCH-bound) [i]
- linear OA(271, 127, F2, 23) (dual of [127, 56, 24]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(21, 8, F2, 1) (dual of [8, 7, 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
- 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(289, 142, F2, 28) (dual of [142, 53, 29]-code) | [i] | Truncation | |
| 2 | Linear OOA(290, 71, F2, 2, 29) (dual of [(71, 2), 52, 30]-NRT-code) | [i] | OOA Folding | |