Information on Result #713266
Linear OA(737, 366, F7, 12) (dual of [366, 329, 13]-code), using construction XX applied to C1 = C([338,4]), C2 = C([0,7]), C3 = C1 + C2 = C([0,4]), and C∩ = C1 ∩ C2 = C([338,7]) based on
- linear OA(725, 342, F7, 9) (dual of [342, 317, 10]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,4}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(719, 342, F7, 8) (dual of [342, 323, 9]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,7], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(731, 342, F7, 12) (dual of [342, 311, 13]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−4,−3,…,7}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(713, 342, F7, 5) (dual of [342, 329, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(74, 16, F7, 3) (dual of [16, 12, 4]-code or 16-cap in PG(3,7)), using
- linear OA(72, 8, F7, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,7)), using
- extended Reed–Solomon code RSe(6,7) [i]
- Hamming code H(2,7) [i]
- algebraic-geometric code AG(F, Q+1P) 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.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(737, 183, F7, 2, 12) (dual of [(183, 2), 329, 13]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(737, 122, F7, 3, 12) (dual of [(122, 3), 329, 13]-NRT-code) | [i] | ||