Information on Result #1297380

Linear OA(2200, 569, F2, 42) (dual of [569, 369, 43]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2193, 559, F2, 43) (dual of [559, 366, 44]-code), using
    • construction XX applied to C1 = C([507,34]), C2 = C([0,38]), C3 = C1 + C2 = C([0,34]), and C∩ = C1 ∩ C2 = C([507,38]) [i] based on
      1. linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,34}, and designed minimum distance d ≥ |I|+1 = 40 [i]
      2. linear OA(2163, 511, F2, 39) (dual of [511, 348, 40]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,38], and designed minimum distance d ≥ |I|+1 = 40 [i]
      3. linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−4,−3,…,38}, and designed minimum distance d ≥ |I|+1 = 44 [i]
      4. linear OA(2145, 511, F2, 35) (dual of [511, 366, 36]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,34], and designed minimum distance d ≥ |I|+1 = 36 [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(2193, 562, F2, 38) (dual of [562, 369, 39]-code), using Gilbert–VarÅ¡amov bound and bm = 2193 > Vbs−1(k−1) = 11951 352724 579141 255593 185145 116623 698868 711992 121968 291634 [i]
  3. linear OA(24, 7, F2, 3) (dual of [7, 3, 4]-code or 7-cap in PG(3,2)), 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(2201, 570, F2, 43) (dual of [570, 369, 44]-code) [i]Adding a Parity Check Bit