Information on Result #701403

Linear OA(740, 66, F7, 21) (dual of [66, 26, 22]-code), using construction XX applied to C1 = C({1,2,4,5,6,8,9,10,11,12,13,16,17,18,19,20}), C2 = C([0,16]), C3 = C1 + C2 = C({1,2,4,5,6,8,9,10,11,12,13,16}), and C∩ = C1 ∩ C2 = C([0,20]) based on
  1. linear OA(730, 48, F7, 17) (dual of [48, 18, 18]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,4,5,6,8,9,10,11,12,13,16,17,18,19,20}, and minimum distance d ≥ |{4,5,…,20}|+1 = 18 (BCH-bound) [i]
  2. linear OA(725, 48, F7, 17) (dual of [48, 23, 18]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,16], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 25 [i]
  4. linear OA(722, 48, F7, 13) (dual of [48, 26, 14]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,4,5,6,8,9,10,11,12,13,16}, and minimum distance d ≥ |{4,5,…,16}|+1 = 14 (BCH-bound) [i]
  5. linear OA(74, 12, F7, 3) (dual of [12, 8, 4]-code or 12-cap in PG(3,7)), using
  6. linear OA(73, 6, F7, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,7) or 6-cap in PG(2,7)), using

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:

ResultThis
result
only		Method
1Linear OOA(740, 33, F7, 2, 21) (dual of [(33, 2), 26, 22]-NRT-code) [i]OOA Folding
2Linear OOA(740, 22, F7, 3, 21) (dual of [(22, 3), 26, 22]-NRT-code) [i]