Information on Result #1297306

Linear OA(2165, 281, F2, 46) (dual of [281, 116, 47]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2159, 274, F2, 46) (dual of [274, 115, 47]-code), using
    • construction XX applied to C1 = C([253,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([253,44]) [i] based on
      1. linear OA(2149, 255, F2, 45) (dual of [255, 106, 46]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,42}, and designed minimum distance d ≥ |I|+1 = 46 [i]
      2. linear OA(2148, 255, F2, 44) (dual of [255, 107, 45]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,44], and designed minimum distance d ≥ |I|+1 = 45 [i]
      3. linear OA(2157, 255, F2, 47) (dual of [255, 98, 48]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,44}, and designed minimum distance d ≥ |I|+1 = 48 [i]
      4. linear OA(2140, 255, F2, 42) (dual of [255, 115, 43]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,42], and designed minimum distance d ≥ |I|+1 = 43 [i]
      5. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
      6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
  2. linear OA(2159, 275, F2, 40) (dual of [275, 116, 41]-code), using Gilbert–VarÅ¡amov bound and bm = 2159 > Vbs−1(k−1) = 404486 046072 585261 542441 273026 846628 888623 618976 [i]
  3. linear OA(25, 6, F2, 5) (dual of [6, 1, 6]-code or 6-arc in PG(4,2)), 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(2166, 282, F2, 47) (dual of [282, 116, 48]-code) [i]Adding a Parity Check Bit