Information on Result #701526
Linear OA(748, 58, F7, 34) (dual of [58, 10, 35]-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}), C2 = C([0,32]), C3 = C1 + C2 = C({1,2,3,4,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32}), and C∩ = C1 ∩ C2 = C([0,33]) based on
- linear OA(740, 48, F7, 28) (dual of [48, 8, 29]-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}, and minimum distance d ≥ |{6,7,…,33}|+1 = 29 (BCH-bound) [i]
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(743, 48, F7, 34) (dual of [48, 5, 35]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,33], and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-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}, and minimum distance d ≥ |{6,7,…,32}|+1 = 28 (BCH-bound) [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- 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]
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(748, 29, F7, 2, 34) (dual of [(29, 2), 10, 35]-NRT-code) | [i] | OOA Folding | |