Information on Result #1297809

Linear OA(2260, 565, F2, 58) (dual of [565, 305, 59]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2255, 558, F2, 58) (dual of [558, 303, 59]-code), using
    • 1 times truncation [i] based on linear OA(2256, 559, F2, 59) (dual of [559, 303, 60]-code), using
      • construction XX applied to C1 = C([507,50]), C2 = C([0,54]), C3 = C1 + C2 = C([0,50]), and C∩ = C1 ∩ C2 = C([507,54]) [i] based on
        1. linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,50}, and designed minimum distance d ≥ |I|+1 = 56 [i]
        2. linear OA(2226, 511, F2, 55) (dual of [511, 285, 56]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,54], and designed minimum distance d ≥ |I|+1 = 56 [i]
        3. linear OA(2244, 511, F2, 59) (dual of [511, 267, 60]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,54}, and designed minimum distance d ≥ |I|+1 = 60 [i]
        4. linear OA(2208, 511, F2, 51) (dual of [511, 303, 52]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,50], and designed minimum distance d ≥ |I|+1 = 52 [i]
        5. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)), using
        6. linear OA(26, 24, F2, 3) (dual of [24, 18, 4]-code or 24-cap in PG(5,2)) (see above)
  2. linear OA(2255, 560, F2, 55) (dual of [560, 305, 56]-code), using Gilbert–VarÅ¡amov bound and bm = 2255 > Vbs−1(k−1) = 7884 496453 113561 413167 472447 205154 862647 744366 336964 344452 785081 177079 062752 [i]
  3. linear OA(23, 5, F2, 2) (dual of [5, 2, 3]-code), 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.