Information on Result #701408

Linear OA(747, 72, F7, 26) (dual of [72, 25, 27]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,20,27,34,40,41}), C2 = C([1,17]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,20,27,34,40,41}) based on
  1. linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,15}|+1 = 25 (BCH-bound) [i]
  2. linear OA(726, 48, F7, 17) (dual of [48, 22, 18]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
  3. linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,20,27,34,40,41}, and minimum distance d ≥ |{−8,−7,…,17}|+1 = 27 (BCH-bound) [i]
  4. linear OA(723, 48, F7, 15) (dual of [48, 25, 16]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 16 [i]
  5. linear OA(710, 20, F7, 8) (dual of [20, 10, 9]-code), using
  6. linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), 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 OA(748, 73, F7, 26) (dual of [73, 25, 27]-code) [i]Code Embedding in Larger Space
2Linear OA(746, 71, F7, 25) (dual of [71, 25, 26]-code) [i]Truncation
3Linear OOA(747, 36, F7, 2, 26) (dual of [(36, 2), 25, 27]-NRT-code) [i]OOA Folding
4Linear OOA(747, 24, F7, 3, 26) (dual of [(24, 3), 25, 27]-NRT-code) [i]