Information on Result #712512
Linear OA(753, 64, F7, 36) (dual of [64, 11, 37]-code), using construction XX applied to C1 = C([41,24]), C2 = C([0,31]), C3 = C1 + C2 = C([0,24]), and C∩ = C1 ∩ C2 = C([41,31]) based on
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,24}, and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,27], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,31}, and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(734, 48, F7, 25) (dual of [48, 14, 26]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,24], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), using
- extended Reed–Solomon code RSe(3,7) [i]
- the expurgated narrow-sense BCH-code C(I) with length 8 | 72−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (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(753, 32, F7, 2, 36) (dual of [(32, 2), 11, 37]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(753, 21, F7, 3, 36) (dual of [(21, 3), 10, 37]-NRT-code) | [i] | ||