Information on Result #701320

Linear OA(711, 52, F7, 6) (dual of [52, 41, 7]-code), using construction XX applied to C1 = C({0,1,2,3,41}), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,41}) based on
  1. linear OA(79, 48, F7, 5) (dual of [48, 39, 6]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,41}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
  2. linear OA(79, 48, F7, 5) (dual of [48, 39, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
  3. linear OA(711, 48, F7, 6) (dual of [48, 37, 7]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,41}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
  4. linear OA(77, 48, F7, 4) (dual of [48, 41, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
  5. linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
  6. linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code) (see above)

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 OA(7108, 5764853, F7, 15) (dual of [5764853, 5764745, 16]-code) [i]Construction X with Extended Narrow-Sense BCH Codes
2Linear OA(7110, 823595, F7, 17) (dual of [823595, 823485, 18]-code) [i]
3Linear OA(7103, 823595, F7, 16) (dual of [823595, 823492, 17]-code) [i]
4Linear OA(796, 823595, F7, 15) (dual of [823595, 823499, 16]-code) [i]
5Linear OOA(711, 26, F7, 2, 6) (dual of [(26, 2), 41, 7]-NRT-code) [i]OOA Folding