Information on Result #661434
Linear OA(2215, 231, F2, 97) (dual of [231, 16, 98]-code), using concatenation of two codes based on
- linear OA(469, 77, F4, 48) (dual of [77, 8, 49]-code), using
- strength reduction [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
- strength reduction [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(2214, 230, F2, 96) (dual of [230, 16, 97]-code) | [i] | Truncation | |
| 2 | Linear OA(2213, 229, F2, 95) (dual of [229, 16, 96]-code) | [i] | ||
| 3 | Linear OA(2211, 227, F2, 93) (dual of [227, 16, 94]-code) | [i] | ||
| 4 | Linear OA(2210, 226, F2, 92) (dual of [226, 16, 93]-code) | [i] | ||
| 5 | Linear OA(2207, 223, F2, 89) (dual of [223, 16, 90]-code) | [i] | ||