Information on Result #1297825

Linear OA(2258, 563, F2, 58) (dual of [563, 305, 59]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2256, 560, F2, 58) (dual of [560, 304, 59]-code), using
    • construction XX applied to C1 = C([507,50]), C2 = C([1,54]), C3 = C1 + C2 = C([1,50]), 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(2225, 511, F2, 54) (dual of [511, 286, 55]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,54], and designed minimum distance d ≥ |I|+1 = 55 [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(2207, 511, F2, 50) (dual of [511, 304, 51]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,50], and designed minimum distance d ≥ |I|+1 = 51 [i]
      5. linear OA(26, 25, F2, 3) (dual of [25, 19, 4]-code or 25-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)), using
  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, 2, F2, 1) (dual of [2, 1, 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

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2259, 564, F2, 59) (dual of [564, 305, 60]-code) [i]Adding a Parity Check Bit