Information on Result #1297569

Linear OA(2228, 576, F2, 48) (dual of [576, 348, 49]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2225, 571, F2, 48) (dual of [571, 346, 49]-code), using
    • construction XX applied to C1 = C([505,38]), C2 = C([0,42]), C3 = C1 + C2 = C([0,38]), and C∩ = C1 ∩ C2 = C([505,42]) [i] based on
      1. linear OA(2190, 511, F2, 45) (dual of [511, 321, 46]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,38}, and designed minimum distance d ≥ |I|+1 = 46 [i]
      2. linear OA(2181, 511, F2, 43) (dual of [511, 330, 44]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,42], and designed minimum distance d ≥ |I|+1 = 44 [i]
      3. linear OA(2208, 511, F2, 49) (dual of [511, 303, 50]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,42}, and designed minimum distance d ≥ |I|+1 = 50 [i]
      4. 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]
      5. linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), 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(2225, 573, F2, 46) (dual of [573, 348, 47]-code), using Gilbert–VarÅ¡amov bound and bm = 2225 > Vbs−1(k−1) = 18 691947 066569 914136 050795 768899 863060 346971 879202 571413 971894 995196 [i]
  3. linear OA(21, 3, F2, 1) (dual of [3, 2, 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(2229, 577, F2, 49) (dual of [577, 348, 50]-code) [i]Adding a Parity Check Bit