Information on Result #677626

Linear OA(393, 106, F3, 53) (dual of [106, 13, 54]-code), using construction XX applied to C1 = C([0,81]), C2 = C([1,105]), C3 = C1 + C2 = C([1,81]), and C∩ = C1 ∩ C2 = C([0,105]) based on
  1. linear OA(366, 80, F3, 41) (dual of [80, 14, 42]-code), using contraction [i] based on linear OA(3146, 160, F3, 83) (dual of [160, 14, 84]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,81], and minimum distance d ≥ |{−1,0,…,81}|+1 = 84 (BCH-bound) [i]
  2. linear OA(375, 80, F3, 52) (dual of [80, 5, 53]-code), using contraction [i] based on linear OA(3155, 160, F3, 105) (dual of [160, 5, 106]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,105], and designed minimum distance d ≥ |I|+1 = 106 [i]
  3. linear OA(376, 80, F3, 53) (dual of [80, 4, 54]-code), using contraction [i] based on linear OA(3156, 160, F3, 107) (dual of [160, 4, 108]-code), using the expurgated narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [0,105], and minimum distance d ≥ |{−5,8,21,…,−67}|+1 = 108 (BCH-bound) [i]
  4. linear OA(365, 80, F3, 40) (dual of [80, 15, 41]-code), using contraction [i] based on linear OA(3145, 160, F3, 81) (dual of [160, 15, 82]-code), using the narrow-sense BCH-code C(I) with length 160 | 38−1, defining interval I = [1,81], and designed minimum distance d ≥ |I|+1 = 82 [i]
  5. linear OA(30, 1, F3, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(317, 25, F3, 11) (dual of [25, 8, 12]-code), using
    • 3 times truncation [i] based on linear OA(320, 28, F3, 14) (dual of [28, 8, 15]-code), using
      • contraction [i] based on linear OA(348, 56, F3, 29) (dual of [56, 8, 30]-code), using the BCH-code C(I) with length 56 | 36−1, defining interval I = {0,1,…,28}, and designed minimum distance d ≥ |I|+1 = 30 [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(393, 53, F3, 2, 53) (dual of [(53, 2), 13, 54]-NRT-code) [i]OOA Folding