Information on Result #1301456

Linear OA(574, 139, F5, 34) (dual of [139, 65, 35]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(568, 130, F5, 34) (dual of [130, 62, 35]-code), using
    • construction XX applied to C1 = C([123,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([123,32]) [i] based on
      1. linear OA(565, 124, F5, 33) (dual of [124, 59, 34]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
      2. linear OA(565, 124, F5, 33) (dual of [124, 59, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
      3. linear OA(568, 124, F5, 34) (dual of [124, 56, 35]-code), using the primitive BCH-code C(I) with length 124 = 53−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
      4. linear OA(562, 124, F5, 32) (dual of [124, 62, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 124 = 53−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
      5. linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code), using
      6. linear OA(50, 3, F5, 0) (dual of [3, 3, 1]-code) (see above)
  2. linear OA(568, 133, F5, 30) (dual of [133, 65, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 568 > Vbs−1(k−1) = 39559 758129 896508 362049 790210 560326 430757 773425 [i]
  3. linear OA(53, 6, F5, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,5) or 6-cap in PG(2,5)), using

Mode: 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.