Information on Result #712466
Linear OA(753, 72, F7, 31) (dual of [72, 19, 32]-code), using construction XX applied to C1 = C([6,31]), C2 = C([1,23]), C3 = C1 + C2 = C([6,23]), and C∩ = C1 ∩ C2 = C([1,31]) based on
- linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,31}, and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(732, 48, F7, 23) (dual of [48, 16, 24]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(739, 48, F7, 31) (dual of [48, 9, 32]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(728, 48, F7, 18) (dual of [48, 20, 19]-code), using the primitive BCH-code C(I) with length 48 = 72−1, defining interval I = {6,7,…,23}, and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(79, 17, F7, 7) (dual of [17, 8, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- extended quadratic residue code Qe(20,7) [i]
- 1 times truncation [i] based on linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(79, 19, F7, 7) (dual of [19, 10, 8]-code), using
- linear OA(74, 7, F7, 4) (dual of [7, 3, 5]-code or 7-arc in PG(3,7)), using
- Reed–Solomon code RS(3,7) [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 OOA(753, 36, F7, 2, 31) (dual of [(36, 2), 19, 32]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(753, 24, F7, 3, 31) (dual of [(24, 3), 19, 32]-NRT-code) | [i] | ||