Information on Result #681997

Linear OA(458, 81, F4, 30) (dual of [81, 23, 31]-code), using construction XX applied to C1 = C([0,68]), C2 = C([1,89]), C3 = C1 + C2 = C([1,68]), and C∩ = C1 ∩ C2 = C([0,89]) based on
  1. 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]
  2. linear OA(449, 63, F4, 29) (dual of [63, 14, 30]-code), using contraction [i] based on linear OA(4175, 189, F4, 89) (dual of [189, 14, 90]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,89], and designed minimum distance d ≥ |I|+1 = 90 [i]
  3. linear OA(450, 63, F4, 30) (dual of [63, 13, 31]-code), using contraction [i] based on linear OA(4176, 189, F4, 92) (dual of [189, 13, 93]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,89], and minimum distance d ≥ |{−2,−1,…,89}|+1 = 93 (BCH-bound) [i]
  4. 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]
  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(458, 27, F4, 3, 30) (dual of [(27, 3), 23, 31]-NRT-code) [i]OOA Folding