Information on Result #685824
Linear OA(744, 56, F7, 31) (dual of [56, 12, 32]-code), using construction X applied to C([0,63]) ⊂ C([0,51]) based on
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,63], and minimum distance d ≥ |{−1,0,…,63}|+1 = 66 (BCH-bound) [i]
- linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using contraction [i] based on linear OA(784, 96, F7, 53) (dual of [96, 12, 54]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,51], and minimum distance d ≥ |{−1,0,…,51}|+1 = 54 (BCH-bound) [i]
- linear OA(74, 8, F7, 4) (dual of [8, 4, 5]-code or 8-arc in PG(3,7)), using
- extended Reed–Solomon code RSe(4,7) [i]
- algebraic-geometric code AG(F, Q+0P) with degQ = 3 and degPÂ =Â 2 [i] based on function field F/F7 with g(F) = 0 and N(F) ≥ 8, using the rational function field F7(x) [i]
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 OOA(744, 28, F7, 2, 31) (dual of [(28, 2), 12, 32]-NRT-code) | [i] | OOA Folding | |