Information on Result #1299762

Linear OA(448, 78, F4, 23) (dual of [78, 30, 24]-code), using construction X with VarÅ¡amov bound based on
  1. linear OA(442, 69, F4, 23) (dual of [69, 27, 24]-code), using
    • construction XX applied to C1 = C([0,62]), C2 = C([1,68]), C3 = C1 + C2 = C([1,62]), and C∩ = C1 ∩ C2 = C([0,68]) [i] based on
      1. linear OA(437, 63, F4, 21) (dual of [63, 26, 22]-code), using contraction [i] based on linear OA(4163, 189, F4, 65) (dual of [189, 26, 66]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,62], and minimum distance d ≥ |{−2,−1,…,62}|+1 = 66 (BCH-bound) [i]
      2. linear OA(440, 63, F4, 22) (dual of [63, 23, 23]-code), using contraction [i] based on linear OA(4166, 189, F4, 68) (dual of [189, 23, 69]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,68], and designed minimum distance d ≥ |I|+1 = 69 [i]
      3. linear OA(441, 63, F4, 23) (dual of [63, 22, 24]-code), using contraction [i] based on linear OA(4167, 189, F4, 71) (dual of [189, 22, 72]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,68], and minimum distance d ≥ |{−2,−1,…,68}|+1 = 72 (BCH-bound) [i]
      4. linear OA(436, 63, F4, 20) (dual of [63, 27, 21]-code), using contraction [i] based on linear OA(4162, 189, F4, 62) (dual of [189, 27, 63]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,62], and designed minimum distance d ≥ |I|+1 = 63 [i]
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
      6. linear OA(41, 5, F4, 1) (dual of [5, 4, 2]-code), using
  2. linear OA(442, 72, F4, 19) (dual of [72, 30, 20]-code), using Gilbert–VarÅ¡amov bound and bm = 442 > Vbs−1(k−1) = 13 528560 897496 211029 336420 [i]
  3. linear OA(43, 6, F4, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), 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.

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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(449, 80, F4, 23) (dual of [80, 31, 24]-code) [i]Construction X with VarÅ¡amov Bound