Information on Result #714993

Linear OA(822, 517, F8, 8) (dual of [517, 495, 9]-code), using construction XX applied to C1 = C([510,5]), C2 = C([0,6]), C3 = C1 + C2 = C([0,5]), and C∩ = C1 ∩ C2 = C([510,6]) based on
  1. linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,5}, and designed minimum distance d ≥ |I|+1 = 8 [i]
  2. linear OA(819, 511, F8, 7) (dual of [511, 492, 8]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
  3. linear OA(822, 511, F8, 8) (dual of [511, 489, 9]-code), using the primitive BCH-code C(I) with length 511 = 83−1, defining interval I = {−1,0,…,6}, and designed minimum distance d ≥ |I|+1 = 9 [i]
  4. linear OA(816, 511, F8, 6) (dual of [511, 495, 7]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 83−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
  5. linear OA(80, 3, F8, 0) (dual of [3, 3, 1]-code), using
  6. linear OA(80, 3, F8, 0) (dual of [3, 3, 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OOA(822, 517, F8, 2, 8) (dual of [(517, 2), 1012, 9]-NRT-code) [i]Embedding of OOA with Gilbert–VarÅ¡amov Bound
2Linear OOA(822, 517, F8, 3, 8) (dual of [(517, 3), 1529, 9]-NRT-code) [i]
3Digital (14, 22, 517)-net over F8 [i]
4Linear OA(823, 539, F8, 8) (dual of [539, 516, 9]-code) [i]VarÅ¡amov–Edel Lengthening
5Linear OA(824, 630, F8, 8) (dual of [630, 606, 9]-code) [i]
6Linear OOA(822, 258, F8, 2, 8) (dual of [(258, 2), 494, 9]-NRT-code) [i]OOA Folding
7Linear OOA(822, 172, F8, 3, 8) (dual of [(172, 3), 494, 9]-NRT-code) [i]