Information on Result #1297340

Linear OA(2176, 292, F2, 48) (dual of [292, 116, 49]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2172, 287, F2, 48) (dual of [287, 115, 49]-code), using
    • construction XX applied to C1 = C([251,42]), C2 = C([1,44]), C3 = C1 + C2 = C([1,42]), and C∩ = C1 ∩ C2 = C([251,44]) [i] based on
      1. 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 = {−4,−3,…,42}, and designed minimum distance d ≥ |I|+1 = 48 [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(2165, 255, F2, 49) (dual of [255, 90, 50]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−4,−3,…,44}, and designed minimum distance d ≥ |I|+1 = 50 [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(26, 23, F2, 3) (dual of [23, 17, 4]-code or 23-cap in PG(5,2)), using
      6. linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
  2. linear OA(2172, 288, F2, 44) (dual of [288, 116, 45]-code), using Gilbert–VarÅ¡amov bound and bm = 2172 > Vbs−1(k−1) = 3561 956325 049204 460125 430421 491274 685162 633222 597632 [i]
  3. linear OA(23, 4, F2, 3) (dual of [4, 1, 4]-code or 4-arc in PG(2,2) or 4-cap in PG(2,2)), 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(2177, 293, F2, 49) (dual of [293, 116, 50]-code) [i]Adding a Parity Check Bit