Information on Result #835998
Linear OOA(523, 15, F5, 2, 16) (dual of [(15, 2), 7, 17]-NRT-code), using OOA 2-folding based on linear OA(523, 30, F5, 16) (dual of [30, 7, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(523, 31, F5, 16) (dual of [31, 8, 17]-code), using
- construction XX applied to C1 = C([0,51]), C2 = C([1,71]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,71]) [i] based on
- linear OA(517, 24, F5, 13) (dual of [24, 7, 14]-code), using contraction [i] based on linear OA(589, 96, F5, 55) (dual of [96, 7, 56]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,51], and minimum distance d ≥ |{−3,−2,…,51}|+1 = 56 (BCH-bound) [i]
- linear OA(520, 24, F5, 17) (dual of [24, 4, 18]-code), using contraction [i] based on linear OA(592, 96, F5, 71) (dual of [96, 4, 72]-code), using the narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,71], and designed minimum distance d ≥ |I|+1 = 72 [i]
- linear OA(521, 24, F5, 18) (dual of [24, 3, 19]-code), using contraction [i] based on linear OA(593, 96, F5, 75) (dual of [96, 3, 76]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [0,71], and minimum distance d ≥ |{−3,−2,…,71}|+1 = 76 (BCH-bound) [i]
- 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 narrow-sense BCH-code C(I) with length 96 | 58−1, defining interval I = [1,51], and designed minimum distance d ≥ |I|+1 = 52 [i]
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(52, 6, F5, 2) (dual of [6, 4, 3]-code or 6-arc in PG(1,5)), using
- extended Reed–Solomon code RSe(4,5) [i]
- Hamming code H(2,5) [i]
- construction XX applied to C1 = C([0,51]), C2 = C([1,71]), C3 = C1 + C2 = C([1,51]), and C∩ = C1 ∩ C2 = C([0,71]) [i] based on
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.
Other Results with Identical Parameters
None.
Depending Results
None.