Information on Result #684370

Linear OA(520, 29, F5, 14) (dual of [29, 9, 15]-code), using construction XX applied to C1 = C([0,47]), C2 = C([1,55]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([0,55]) based on
  1. linear OA(516, 24, F5, 12) (dual of [24, 8, 13]-code), using contraction [i] based on linear OA(588, 96, F5, 51) (dual of [96, 8, 52]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,47], and minimum distance d ≥ |{−3,−2,…,47}|+1 = 52 (BCH-bound) [i]
  2. linear OA(518, 24, F5, 13) (dual of [24, 6, 14]-code), using contraction [i] based on linear OA(590, 96, F5, 55) (dual of [96, 6, 56]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,55], and designed minimum distance d ≥ |I|+1 = 56 [i]
  3. linear OA(519, 24, F5, 14) (dual of [24, 5, 15]-code), using contraction [i] based on linear OA(591, 96, F5, 59) (dual of [96, 5, 60]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,55], and minimum distance d ≥ |{−3,−2,…,55}|+1 = 60 (BCH-bound) [i]
  4. linear OA(515, 24, F5, 11) (dual of [24, 9, 12]-code), using contraction [i] based on linear OA(587, 96, F5, 47) (dual of [96, 9, 48]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
  5. linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
  6. linear OA(51, 4, F5, 1) (dual of [4, 3, 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(519, 28, F5, 13) (dual of [28, 9, 14]-code) [i]Truncation