Information on Result #701499

Linear OA(740, 52, F7, 28) (dual of [52, 12, 29]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,41}), C2 = C([0,26]), C3 = C1 + C2 = C([0,25]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,41}) based on
  1. 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 = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,41}, and minimum distance d ≥ |{−1,0,…,25}|+1 = 28 (BCH-bound) [i]
  2. linear OA(738, 48, F7, 27) (dual of [48, 10, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [i]
  3. 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 = {0,1,2,3,4,5,6,8,9,10,11,12,13,16,17,18,19,20,24,25,26,41}, and minimum distance d ≥ |{−1,0,…,26}|+1 = 29 (BCH-bound) [i]
  4. linear OA(736, 48, F7, 26) (dual of [48, 12, 27]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [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 OOA(740, 26, F7, 2, 28) (dual of [(26, 2), 12, 29]-NRT-code) [i]OOA Folding
2Linear OOA(740, 17, F7, 3, 28) (dual of [(17, 3), 11, 29]-NRT-code) [i]