Information on Result #712175

Linear OA(5142, 675, F5, 40) (dual of [675, 533, 41]-code), using construction XX applied to C1 = C([121,156]), C2 = C([128,161]), C3 = C1 + C2 = C([128,156]), and C∩ = C1 ∩ C2 = C([121,161]) based on
  1. linear OA(5111, 624, F5, 36) (dual of [624, 513, 37]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,156}, and designed minimum distance d ≥ |I|+1 = 37 [i]
  2. linear OA(5107, 624, F5, 34) (dual of [624, 517, 35]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,161}, and designed minimum distance d ≥ |I|+1 = 35 [i]
  3. linear OA(5127, 624, F5, 41) (dual of [624, 497, 42]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,161}, and designed minimum distance d ≥ |I|+1 = 42 [i]
  4. linear OA(591, 624, F5, 29) (dual of [624, 533, 30]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,156}, and designed minimum distance d ≥ |I|+1 = 30 [i]
  5. linear OA(511, 31, F5, 6) (dual of [31, 20, 7]-code), using
    • construction X applied to Ce(5) ⊂ Ce(2) [i] based on
      1. linear OA(59, 25, F5, 6) (dual of [25, 16, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
      2. linear OA(55, 25, F5, 3) (dual of [25, 20, 4]-code or 25-cap in PG(4,5)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
      3. linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
  6. linear OA(54, 20, F5, 3) (dual of [20, 16, 4]-code or 20-cap in PG(3,5)), 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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(5143, 676, F5, 40) (dual of [676, 533, 41]-code) [i]Code Embedding in Larger Space
2Linear OOA(5142, 337, F5, 2, 40) (dual of [(337, 2), 532, 41]-NRT-code) [i]OOA Folding
3Linear OOA(5142, 225, F5, 3, 40) (dual of [(225, 3), 533, 41]-NRT-code) [i]