Information on Result #1297282

Linear OA(2153, 301, F2, 38) (dual of [301, 148, 39]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(2150, 297, F2, 38) (dual of [297, 147, 39]-code), using
    • construction XX applied to C1 = C([219,254]), C2 = C([227,2]), C3 = C1 + C2 = C([227,254]), and C∩ = C1 ∩ C2 = C([219,2]) [i] based on
      1. linear OA(2124, 255, F2, 36) (dual of [255, 131, 37]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−36,−35,…,−1}, and designed minimum distance d ≥ |I|+1 = 37 [i]
      2. linear OA(2117, 255, F2, 31) (dual of [255, 138, 32]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,2}, and designed minimum distance d ≥ |I|+1 = 32 [i]
      3. 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 = {−36,−35,…,2}, and designed minimum distance d ≥ |I|+1 = 40 [i]
      4. linear OA(2108, 255, F2, 28) (dual of [255, 147, 29]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−28,−27,…,−1}, and designed minimum distance d ≥ |I|+1 = 29 [i]
      5. linear OA(216, 32, F2, 7) (dual of [32, 16, 8]-code), using
      6. linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
  2. linear OA(2150, 298, F2, 35) (dual of [298, 148, 36]-code), using Gilbert–VarÅ¡amov bound and bm = 2150 > Vbs−1(k−1) = 645 769152 051832 049423 495961 051175 984079 703774 [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

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Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(2154, 302, F2, 39) (dual of [302, 148, 40]-code) [i]Adding a Parity Check Bit