Information on Result #731711
Linear OA(2159, 201, F2, 53) (dual of [201, 42, 54]-code), using concatenation of two codes based on
- linear OA(446, 67, F4, 26) (dual of [67, 21, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(446, 68, F4, 26) (dual of [68, 22, 27]-code), using
- construction X applied to C([0,77]) ⊂ C([0,68]) [i] based on
- linear OA(444, 63, F4, 26) (dual of [63, 19, 27]-code), using contraction [i] based on linear OA(4170, 189, F4, 80) (dual of [189, 19, 81]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,77], and minimum distance d ≥ |{−2,−1,…,77}|+1 = 81 (BCH-bound) [i]
- linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using contraction [i] based on linear OA(4167, 189, F4, 71) (dual of [189, 22, 72]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,68], and minimum distance d ≥ |{−2,−1,…,68}|+1 = 72 (BCH-bound) [i]
- linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), using
- extended Reed–Solomon code RSe(3,4) [i]
- Hamming code H(2,4) [i]
- construction X applied to C([0,77]) ⊂ C([0,68]) [i] based on
- discarding factors / shortening the dual code based on linear OA(446, 68, F4, 26) (dual of [68, 22, 27]-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(2158, 200, F2, 52) (dual of [200, 42, 53]-code) | [i] | Truncation | |
| 2 | Linear OOA(2159, 100, F2, 2, 53) (dual of [(100, 2), 41, 54]-NRT-code) | [i] | OOA Folding | |
| 3 | Linear OOA(2159, 67, F2, 3, 53) (dual of [(67, 3), 42, 54]-NRT-code) | [i] | ||