Information on Result #712173

Linear OA(5146, 678, F5, 41) (dual of [678, 532, 42]-code), using construction XX applied to C1 = C([121,155]), C2 = C([128,161]), C3 = C1 + C2 = C([128,155]), and C∩ = C1 ∩ C2 = C([121,161]) 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(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(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(510, 28, F5, 6) (dual of [28, 18, 7]-code), using
    • construction X applied to Ce(5) ⊂ Ce(3) [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(57, 25, F5, 4) (dual of [25, 18, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 24 = 52−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
      3. linear OA(51, 3, F5, 1) (dual of [3, 2, 2]-code), using
  6. linear OA(59, 26, F5, 5) (dual of [26, 17, 6]-code), using
    • the expurgated narrow-sense BCH-code C(I) with length 26 | 54−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]

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.