Information on Result #681992

Linear OA(464, 81, F4, 34) (dual of [81, 17, 35]-code), using construction XX applied to C1 = C([0,80]), C2 = C([1,125]), C3 = C1 + C2 = C([1,80]), and C∩ = C1 ∩ C2 = C([0,125]) based on
  1. linear OA(447, 63, F4, 27) (dual of [63, 16, 28]-code), using contraction [i] based on linear OA(4173, 189, F4, 83) (dual of [189, 16, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,80], and minimum distance d ≥ |{−2,−1,…,80}|+1 = 84 (BCH-bound) [i]
  2. linear OA(455, 63, F4, 41) (dual of [63, 8, 42]-code), using contraction [i] based on linear OA(4181, 189, F4, 125) (dual of [189, 8, 126]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,125], and designed minimum distance d ≥ |I|+1 = 126 [i]
  3. linear OA(456, 63, F4, 42) (dual of [63, 7, 43]-code), using contraction [i] based on linear OA(4182, 189, F4, 128) (dual of [189, 7, 129]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,125], and minimum distance d ≥ |{−2,−1,…,125}|+1 = 129 (BCH-bound) [i]
  4. linear OA(446, 63, F4, 26) (dual of [63, 17, 27]-code), using contraction [i] based on linear OA(4172, 189, F4, 80) (dual of [189, 17, 81]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,80], and designed minimum distance d ≥ |I|+1 = 81 [i]
  5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(48, 17, F4, 6) (dual of [17, 9, 7]-code), using
    • the BCH-code C(I) with length 17 | 44−1, defining interval I = {1,4,7,…,16}, and designed minimum distance d ≥ |I|+1 = 7 [i]

Mode: Constructive and 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 OOA(464, 27, F4, 3, 34) (dual of [(27, 3), 17, 35]-NRT-code) [i]OOA Folding