Information on Result #731725
Linear OA(2212, 228, F2, 97) (dual of [228, 16, 98]-code), using concatenation of two codes based on
- linear OA(468, 76, F4, 48) (dual of [76, 8, 49]-code), using
- 1 times truncation [i] based on linear OA(469, 77, F4, 49) (dual of [77, 8, 50]-code), using
- construction X applied to C([0,25]) ⊂ C([0,21]) [i] based on
- linear OA(463, 65, F4, 51) (dual of [65, 2, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,25], and minimum distance d ≥ |{−15,−4,7,…,15}|+1 = 52 (BCH-bound) [i]
- linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
- linear OA(46, 12, F4, 5) (dual of [12, 6, 6]-code), using
- extended quadratic residue code Qe(12,4) [i]
- construction X applied to C([0,25]) ⊂ C([0,21]) [i] based on
- 1 times truncation [i] based on linear OA(469, 77, F4, 49) (dual of [77, 8, 50]-code), using
- linear OA(21, 3, F2, 1) (dual of [3, 2, 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.
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(2212, 228, F2, 96) (dual of [228, 16, 97]-code) | [i] | Strength Reduction | |
| 2 | Linear OA(2212, 228, F2, 95) (dual of [228, 16, 96]-code) | [i] | ||
| 3 | Linear OA(2212, 228, F2, 94) (dual of [228, 16, 95]-code) | [i] | ||
| 4 | Linear OA(2212, 228, F2, 93) (dual of [228, 16, 94]-code) | [i] | ||
| 5 | Linear OA(2212, 228, F2, 92) (dual of [228, 16, 93]-code) | [i] | ||
| 6 | Linear OA(2211, 227, F2, 96) (dual of [227, 16, 97]-code) | [i] | Truncation | |
| 7 | Linear OA(2210, 226, F2, 95) (dual of [226, 16, 96]-code) | [i] | ||
| 8 | Linear OA(2208, 224, F2, 93) (dual of [224, 16, 94]-code) | [i] | ||
| 9 | Linear OA(2207, 223, F2, 92) (dual of [223, 16, 93]-code) | [i] | ||
| 10 | Linear OA(2204, 220, F2, 89) (dual of [220, 16, 90]-code) | [i] | ||
| 11 | Linear OOA(2212, 114, F2, 2, 97) (dual of [(114, 2), 16, 98]-NRT-code) | [i] | OOA Folding | |
| 12 | Linear OOA(2212, 76, F2, 3, 97) (dual of [(76, 3), 16, 98]-NRT-code) | [i] | ||