Information on Result #1300615

Linear OA(4189, 271, F4, 88) (dual of [271, 82, 89]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(4184, 263, F4, 88) (dual of [263, 79, 89]-code), using
    • construction XX applied to C1 = C([254,85]), C2 = C([0,86]), C3 = C1 + C2 = C([0,85]), and C∩ = C1 ∩ C2 = C([254,86]) [i] based on
      1. linear OA(4180, 255, F4, 87) (dual of [255, 75, 88]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,85}, and designed minimum distance d ≥ |I|+1 = 88 [i]
      2. linear OA(4180, 255, F4, 87) (dual of [255, 75, 88]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,86], and designed minimum distance d ≥ |I|+1 = 88 [i]
      3. linear OA(4184, 255, F4, 88) (dual of [255, 71, 89]-code), using the primitive BCH-code C(I) with length 255 = 44−1, defining interval I = {−1,0,…,86}, and designed minimum distance d ≥ |I|+1 = 89 [i]
      4. linear OA(4176, 255, F4, 86) (dual of [255, 79, 87]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [0,85], and designed minimum distance d ≥ |I|+1 = 87 [i]
      5. linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
      6. linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code) (see above)
  2. linear OA(4184, 266, F4, 85) (dual of [266, 82, 86]-code), using Gilbert–VarÅ¡amov bound and bm = 4184 > Vbs−1(k−1) = 565 489244 997832 774301 679777 628952 724941 982110 276293 634026 188982 359800 688772 438032 017231 778418 994831 308459 917664 [i]
  3. linear OA(42, 5, F4, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,4)), 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.