Information on Result #1297370

Linear OA(2197, 1081, F2, 36) (dual of [1081, 884, 37]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2191, 1074, F2, 36) (dual of [1074, 883, 37]-code), using
    • construction XX applied to C1 = C([989,1022]), C2 = C([995,2]), C3 = C1 + C2 = C([995,1022]), and C∩ = C1 ∩ C2 = C([989,2]) [i] based on
      1. linear OA(2165, 1023, F2, 34) (dual of [1023, 858, 35]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,−1}, and designed minimum distance d ≥ |I|+1 = 35 [i]
      2. linear OA(2151, 1023, F2, 31) (dual of [1023, 872, 32]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
      3. linear OA(2176, 1023, F2, 37) (dual of [1023, 847, 38]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−34,−33,…,2}, and designed minimum distance d ≥ |I|+1 = 38 [i]
      4. linear OA(2140, 1023, F2, 28) (dual of [1023, 883, 29]-code), using the primitive BCH-code C(I) with length 1023 = 210−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [i]
      5. linear OA(211, 36, F2, 4) (dual of [36, 25, 5]-code), using
      6. linear OA(24, 15, F2, 2) (dual of [15, 11, 3]-code), using
  2. linear OA(2191, 1075, F2, 30) (dual of [1075, 884, 31]-code), using Gilbert–VarÅ¡amov bound and bm = 2191 > Vbs−1(k−1) = 629 705066 860597 099967 497294 461721 637105 802368 368243 286288 [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(2198, 1082, F2, 37) (dual of [1082, 884, 38]-code) [i]Adding a Parity Check Bit