Information on Result #690877

Linear OA(966, 91, F9, 44) (dual of [91, 25, 45]-code), using construction XX applied to C1 = C([0,79]), C2 = C([1,87]), C3 = C1 + C2 = C([1,79]), and C∩ = C1 ∩ C2 = C([0,87]) based on
  1. linear OA(956, 80, F9, 40) (dual of [80, 24, 41]-code), using contraction [i] based on linear OA(9136, 160, F9, 81) (dual of [160, 24, 82]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,79], and minimum distance d ≥ |{−1,0,…,79}|+1 = 82 (BCH-bound) [i]
  2. linear OA(962, 80, F9, 43) (dual of [80, 18, 44]-code), using contraction [i] based on linear OA(9142, 160, F9, 87) (dual of [160, 18, 88]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,87], and designed minimum distance d ≥ |I|+1 = 88 [i]
  3. linear OA(963, 80, F9, 44) (dual of [80, 17, 45]-code), using contraction [i] based on linear OA(9143, 160, F9, 89) (dual of [160, 17, 90]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,87], and minimum distance d ≥ |{−1,0,…,87}|+1 = 90 (BCH-bound) [i]
  4. linear OA(955, 80, F9, 39) (dual of [80, 25, 40]-code), using contraction [i] based on linear OA(9135, 160, F9, 79) (dual of [160, 25, 80]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,79], and designed minimum distance d ≥ |I|+1 = 80 [i]
  5. linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(93, 10, F9, 3) (dual of [10, 7, 4]-code or 10-arc in PG(2,9) or 10-cap in PG(2,9)), 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(966, 91, F9, 43) (dual of [91, 25, 44]-code) [i]Strength Reduction