Information on Result #684366

Linear OA(528, 36, F5, 19) (dual of [36, 8, 20]-code), using construction XX applied to C1 = C([0,51]), C2 = C([1,75]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,75]) based on
  1. linear OA(517, 24, F5, 13) (dual of [24, 7, 14]-code), using contraction [i] based on linear OA(589, 96, F5, 55) (dual of [96, 7, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,51], and minimum distance d ≥ |{−3,−2,…,51}|+1 = 56 (BCH-bound) [i]
  2. linear OA(521, 24, F5, 18) (dual of [24, 3, 19]-code), using contraction [i] based on linear OA(593, 96, F5, 75) (dual of [96, 3, 76]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,75], and designed minimum distance d ≥ |I|+1 = 76 [i]
  3. linear OA(522, 24, F5, 19) (dual of [24, 2, 20]-code), using contraction [i] based on linear OA(594, 96, F5, 79) (dual of [96, 2, 80]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,75], and minimum distance d ≥ |{3,10,17,…,−27}|+1 = 80 (BCH-bound) [i]
  4. linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using contraction [i] based on linear OA(588, 96, F5, 51) (dual of [96, 8, 52]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
  5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(56, 11, F5, 5) (dual of [11, 5, 6]-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(528, 18, F5, 2, 19) (dual of [(18, 2), 8, 20]-NRT-code) [i]OOA Folding