Information on Result #700483
Linear OA(230, 45, F2, 12) (dual of [45, 15, 13]-code), using construction XX applied to C1 = C({1,3,5,11}), C2 = C([1,7]), C3 = C1 + C2 = C([1,5]), and C∩ = C1 ∩ C2 = C([1,11]) based on
- linear OA(220, 31, F2, 8) (dual of [31, 11, 9]-code), using the primitive cyclic code C(A) with length 31 = 25−1, defining set A = {1,3,5,11}, and minimum distance d ≥ |{1,5,9,13,17}| + |{0,1,…,7}∖{1,2,5,6}| = 9 (general Roos-bound) [i]
- linear OA(220, 31, F2, 10) (dual of [31, 11, 11]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(225, 31, F2, 14) (dual of [31, 6, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(215, 31, F2, 6) (dual of [31, 16, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 31 = 25−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 6, F2, 1) (dual of [6, 5, 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(231, 46, F2, 13) (dual of [46, 15, 14]-code) | [i] | Adding a Parity Check Bit | |