Information on Result #701505

Linear OA(751, 63, F7, 34) (dual of [63, 12, 35]-code), using construction XX applied to C1 = C({1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}), C2 = C([1,27]), C3 = C1 + C2 = C({1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}), and C∩ = C1 ∩ C2 = C([1,34]) based on
  1. 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 = {1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27,32,33,34}, and minimum distance d ≥ |{7,8,…,34}|+1 = 29 (BCH-bound) [i]
  2. 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]
  3. 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]
  4. linear OA(735, 48, F7, 25) (dual of [48, 13, 26]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {1,2,3,4,8,9,10,11,12,13,16,17,18,19,20,24,25,26,27}, and minimum distance d ≥ |{7,8,…,31}|+1 = 26 (BCH-bound) [i]
  5. linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
  6. linear OA(75, 8, F7, 5) (dual of [8, 3, 6]-code or 8-arc in PG(4,7)), 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.

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Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(751, 21, F7, 3, 34) (dual of [(21, 3), 12, 35]-NRT-code) [i]OOA Folding