Information on Result #712056

Linear OA(5138, 672, F5, 39) (dual of [672, 534, 40]-code), using construction XX applied to C1 = C([121,155]), C2 = C([128,159]), C3 = C1 + C2 = C([128,155]), and C∩ = C1 ∩ C2 = C([121,159]) based on
  1. linear OA(5110, 624, F5, 35) (dual of [624, 514, 36]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,155}, and designed minimum distance d ≥ |I|+1 = 36 [i]
  2. linear OA(5103, 624, F5, 32) (dual of [624, 521, 33]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,159}, and designed minimum distance d ≥ |I|+1 = 33 [i]
  3. linear OA(5123, 624, F5, 39) (dual of [624, 501, 40]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {121,122,…,159}, and designed minimum distance d ≥ |I|+1 = 40 [i]
  4. linear OA(590, 624, F5, 28) (dual of [624, 534, 29]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {128,129,…,155}, and designed minimum distance d ≥ |I|+1 = 29 [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, 17, F5, 3) (dual of [17, 13, 4]-code or 17-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 OOA(5138, 336, F5, 2, 39) (dual of [(336, 2), 534, 40]-NRT-code) [i]OOA Folding
2Linear OOA(5138, 224, F5, 3, 39) (dual of [(224, 3), 534, 40]-NRT-code) [i]