Information on Result #1297821

Linear OA(2259, 564, F2, 58) (dual of [564, 305, 59]-code), using construction X with VarÅ¡amov bound based on
  1. 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(2256, 561, F2, 56) (dual of [561, 305, 57]-code), using Gilbert–VarÅ¡amov bound and bm = 2256 > Vbs−1(k−1) = 80455 931010 574507 841301 639645 950688 095636 434313 226931 627763 668094 066419 572960 [i]
  3. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-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.