Information on Result #629435

Linear OA(2186, 198, F2, 89) (dual of [198, 12, 90]-code), using concatenation of two codes based on
  1. linear OA(460, 66, F4, 44) (dual of [66, 6, 45]-code), using
    • discarding factors / shortening the dual code based on linear OA(460, 67, F4, 44) (dual of [67, 7, 45]-code), using
      • 3 times truncation [i] based on linear OA(463, 70, F4, 47) (dual of [70, 7, 48]-code), using
        • construction XX applied to C1 = C([0,128]), C2 = C([1,140]), C3 = C1 + C2 = C([1,128]), and C∩ = C1 ∩ C2 = C([0,140]) [i] based on
          1. linear OA(457, 63, F4, 43) (dual of [63, 6, 44]-code), using contraction [i] based on linear OA(4183, 189, F4, 131) (dual of [189, 6, 132]-code), using the expurgated narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [0,128], and minimum distance d ≥ |{−2,−1,…,128}|+1 = 132 (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(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 narrow-sense BCH-code C(I) with length 189 | 49−1, defining interval I = [1,128], and designed minimum distance d ≥ |I|+1 = 129 [i]
          5. linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
          6. 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
  2. linear OA(21, 3, F2, 1) (dual of [3, 2, 2]-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(2185, 197, F2, 88) (dual of [197, 12, 89]-code) [i]Truncation
2Linear OOA(2186, 99, F2, 2, 89) (dual of [(99, 2), 12, 90]-NRT-code) [i]OOA Folding
3Linear OOA(2186, 66, F2, 3, 89) (dual of [(66, 3), 12, 90]-NRT-code) [i]