Information on Result #701511
Linear OA(752, 63, F7, 35) (dual of [63, 11, 36]-code), using construction XX applied to C1 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}), C2 = C([1,27]), C3 = C1 + C2 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), and C∩ = C1 ∩ C2 = C([1,34]) based on
- linear OA(742, 48, F7, 29) (dual of [48, 6, 30]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}, and minimum distance d ≥ |{6,7,…,34}|+1 = 30 (BCH-bound) [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(744, 48, F7, 39) (dual of [48, 4, 40]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(737, 48, F7, 26) (dual of [48, 11, 27]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{6,7,…,31}|+1 = 27 (BCH-bound) [i]
- linear OA(73, 8, F7, 3) (dual of [8, 5, 4]-code or 8-arc in PG(2,7) or 8-cap in PG(2,7)), using
- extended Reed–Solomon code RSe(5,7) [i]
- oval in PG(2, 7) [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 OOA(752, 21, F7, 3, 35) (dual of [(21, 3), 11, 36]-NRT-code) | [i] | OOA Folding | |