Information on Result #712517
Linear OA(753, 63, F7, 37) (dual of [63, 10, 38]-code), using construction XX applied to C1 = C([41,25]), C2 = C([0,31]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C([41,31]) based on
- linear OA(742, 48, F7, 33) (dual of [48, 6, 34]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {−7,−6,…,25}, and designed minimum distance d ≥ |I|+1 = 34 [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(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [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]
- linear OA(75, 7, F7, 5) (dual of [7, 2, 6]-code or 7-arc in PG(4,7)), using
- Reed–Solomon code RS(2,7) [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 OA(752, 62, F7, 36) (dual of [62, 10, 37]-code) | [i] | Truncation | |
| 2 | Linear OOA(753, 21, F7, 3, 37) (dual of [(21, 3), 10, 38]-NRT-code) | [i] | OOA Folding | |