Information on Result #1297501

Linear OA(2219, 575, F2, 46) (dual of [575, 356, 47]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2216, 571, F2, 46) (dual of [571, 355, 47]-code), using
    • construction XX applied to C1 = C([505,36]), C2 = C([0,40]), C3 = C1 + C2 = C([0,36]), and C∩ = C1 ∩ C2 = C([505,40]) [i] based on
      1. 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 = {−6,−5,…,36}, and designed minimum distance d ≥ |I|+1 = 44 [i]
      2. linear OA(2172, 511, F2, 41) (dual of [511, 339, 42]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,40], and designed minimum distance d ≥ |I|+1 = 42 [i]
      3. linear OA(2199, 511, F2, 47) (dual of [511, 312, 48]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−6,−5,…,40}, and designed minimum distance d ≥ |I|+1 = 48 [i]
      4. linear OA(2154, 511, F2, 37) (dual of [511, 357, 38]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [0,36], and designed minimum distance d ≥ |I|+1 = 38 [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(2216, 572, F2, 43) (dual of [572, 356, 44]-code), using Gilbert–VarÅ¡amov bound and bm = 2216 > Vbs−1(k−1) = 9896 462833 581332 279439 061192 197683 605398 891289 322964 465806 889487 [i]
  3. linear OA(22, 3, F2, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,2)), 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(2220, 576, F2, 47) (dual of [576, 356, 48]-code) [i]Adding a Parity Check Bit