Information on Result #731755

Linear OA(4128, 136, F4, 89) (dual of [136, 8, 90]-code), using juxtaposition based on
  1. linear OA(455, 63, F4, 41) (dual of [63, 8, 42]-code), using
    • 2 times truncation [i] based on linear OA(457, 65, F4, 43) (dual of [65, 8, 44]-code), using
      • the expurgated narrow-sense BCH-code C(I) with length 65 | 46−1, defining interval I = [0,21], and minimum distance d ≥ |{−21,−20,…,21}|+1 = 44 (BCH-bound) [i]
  2. linear OA(465, 73, F4, 47) (dual of [73, 8, 48]-code), using
    • construction XX applied to C1 = C([0,125]), C2 = C([1,140]), C3 = C1 + C2 = C([1,125]), and C∩ = C1 ∩ C2 = C([0,140]) [i] based on
      1. 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]
      2. linear OA(459, 63, F4, 46) (dual of [63, 4, 47]-code), using contraction [i] based on linear OA(4185, 189, F4, 140) (dual of [189, 4, 141]-code), using the narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,140], and designed minimum distance d ≥ |I|+1 = 141 [i]
      3. linear OA(460, 63, F4, 47) (dual of [63, 3, 48]-code), using contraction [i] based on linear OA(4186, 189, F4, 143) (dual of [189, 3, 144]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,140], and minimum distance d ≥ |{−7,−2,3,…,−53}|+1 = 144 (BCH-bound) [i]
      4. 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]
      5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
      6. linear OA(45, 9, F4, 4) (dual of [9, 4, 5]-code), using

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.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1Linear OA(4128, 136, F4, 88) (dual of [136, 8, 89]-code) [i]Strength Reduction
2Linear OA(4128, 136, F4, 87) (dual of [136, 8, 88]-code) [i]
3Linear OA(4128, 136, F4, 86) (dual of [136, 8, 87]-code) [i]
4Linear OOA(4128, 68, F4, 2, 89) (dual of [(68, 2), 8, 90]-NRT-code) [i]OOA Folding