Information on Result #711946

Linear OA(5134, 671, F5, 38) (dual of [671, 537, 39]-code), using construction XX applied to C1 = C([617,26]), C2 = C([0,30]), C3 = C1 + C2 = C([0,26]), and C∩ = C1 ∩ C2 = C([617,30]) based on
  1. 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 = {−7,−6,…,26}, and designed minimum distance d ≥ |I|+1 = 35 [i]
  2. linear OA(595, 624, F5, 31) (dual of [624, 529, 32]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,30], and designed minimum distance d ≥ |I|+1 = 32 [i]
  3. linear OA(5119, 624, F5, 38) (dual of [624, 505, 39]-code), using the primitive BCH-code C(I) with length 624 = 54−1, defining interval I = {−7,−6,…,30}, and designed minimum distance d ≥ |I|+1 = 39 [i]
  4. linear OA(583, 624, F5, 27) (dual of [624, 541, 28]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [0,26], and designed minimum distance d ≥ |I|+1 = 28 [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, 16, F5, 3) (dual of [16, 12, 4]-code or 16-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

None.