Information on Result #690853

Linear OA(980, 100, F9, 53) (dual of [100, 20, 54]-code), using construction XX applied to C1 = C([0,85]), C2 = C([1,105]), C3 = C1 + C2 = C([1,85]), and C∩ = C1 ∩ C2 = C([0,105]) based on
  1. linear OA(961, 80, F9, 43) (dual of [80, 19, 44]-code), using contraction [i] based on linear OA(9141, 160, F9, 87) (dual of [160, 19, 88]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,85], and minimum distance d ≥ |{−1,0,…,85}|+1 = 88 (BCH-bound) [i]
  2. linear OA(969, 80, F9, 52) (dual of [80, 11, 53]-code), using contraction [i] based on linear OA(9149, 160, F9, 105) (dual of [160, 11, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [i]
  3. linear OA(970, 80, F9, 53) (dual of [80, 10, 54]-code), using contraction [i] based on linear OA(9150, 160, F9, 107) (dual of [160, 10, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [0,105], and minimum distance d ≥ |{−1,0,…,105}|+1 = 108 (BCH-bound) [i]
  4. linear OA(960, 80, F9, 42) (dual of [80, 20, 43]-code), using contraction [i] based on linear OA(9140, 160, F9, 85) (dual of [160, 20, 86]-code), using the narrow-sense BCH-code C(I) with length 160 | 94−1, defining interval I = [1,85], and designed minimum distance d ≥ |I|+1 = 86 [i]
  5. linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(910, 19, F9, 9) (dual of [19, 9, 10]-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 OOA(980, 50, F9, 2, 53) (dual of [(50, 2), 20, 54]-NRT-code) [i]OOA Folding