Information on Result #717976

Linear OA(973, 118, F9, 39) (dual of [118, 45, 40]-code), using construction XX applied to C1 = C([71,20]), C2 = C([0,29]), C3 = C1 + C2 = C([0,20]), and C∩ = C1 ∩ C2 = C([71,29]) based on
  1. linear OA(945, 80, F9, 30) (dual of [80, 35, 31]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,20}, and designed minimum distance d ≥ |I|+1 = 31 [i]
  2. linear OA(945, 80, F9, 30) (dual of [80, 35, 31]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,29], and designed minimum distance d ≥ |I|+1 = 31 [i]
  3. linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using the primitive BCH-code C(I) with length 80 = 92−1, defining interval I = {−9,−8,…,29}, and designed minimum distance d ≥ |I|+1 = 40 [i]
  4. linear OA(933, 80, F9, 21) (dual of [80, 47, 22]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
  5. linear OA(99, 19, F9, 8) (dual of [19, 10, 9]-code), using
  6. linear OA(99, 19, F9, 8) (dual of [19, 10, 9]-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(973, 118, F9, 38) (dual of [118, 45, 39]-code) [i]Strength Reduction
2Linear OA(975, 120, F9, 39) (dual of [120, 45, 40]-code) [i]Code Embedding in Larger Space
3Linear OA(972, 117, F9, 38) (dual of [117, 45, 39]-code) [i]Truncation
4Linear OA(971, 116, F9, 37) (dual of [116, 45, 38]-code) [i]
5Linear OA(970, 115, F9, 36) (dual of [115, 45, 37]-code) [i]
6Linear OOA(973, 59, F9, 2, 39) (dual of [(59, 2), 45, 40]-NRT-code) [i]OOA Folding