Information on Result #1297272

Linear OA(2149, 281, F2, 40) (dual of [281, 132, 41]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2143, 274, F2, 40) (dual of [274, 131, 41]-code), using
    • construction XX applied to C1 = C([253,36]), C2 = C([1,38]), C3 = C1 + C2 = C([1,36]), and C∩ = C1 ∩ C2 = C([253,38]) [i] based on
      1. linear OA(2133, 255, F2, 39) (dual of [255, 122, 40]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,36}, and designed minimum distance d ≥ |I|+1 = 40 [i]
      2. linear OA(2132, 255, F2, 38) (dual of [255, 123, 39]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
      3. linear OA(2141, 255, F2, 41) (dual of [255, 114, 42]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,38}, and designed minimum distance d ≥ |I|+1 = 42 [i]
      4. linear OA(2124, 255, F2, 36) (dual of [255, 131, 37]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [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(2143, 275, F2, 34) (dual of [275, 132, 35]-code), using Gilbert–VarÅ¡amov bound and bm = 2143 > Vbs−1(k−1) = 4 992234 375931 101959 868202 317988 917568 072376 [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(2150, 282, F2, 41) (dual of [282, 132, 42]-code) [i]Adding a Parity Check Bit