Information on Result #701532
Linear OA(768, 75, F7, 50) (dual of [75, 7, 51]-code), using construction X applied to C([0,31]) ⊂ C([0,29]) based on
- linear OA(756, 57, F7, 56) (dual of [57, 1, 57]-code or 57-arc in PG(55,7)), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,37], and minimum distance d ≥ |{−8,3,14,…,27}|+1 = 57 (BCH-bound) [i]
- linear OA(750, 57, F7, 40) (dual of [57, 7, 41]-code), using the expurgated narrow-sense BCH-code C(I) with length 57 | 73−1, defining interval I = [0,29], and minimum distance d ≥ |{−10,−9,…,29}|+1 = 41 (BCH-bound) [i]
- linear OA(712, 18, F7, 9) (dual of [18, 6, 10]-code), using
- construction XX applied to C1 = C([0,15]), C2 = C([1,17]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C([0,17]) [i] based on
- linear OA(711, 16, F7, 8) (dual of [16, 5, 9]-code), using contraction [i] based on linear OA(727, 32, F7, 17) (dual of [32, 5, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 32 | 74−1, defining interval I = [0,15], and minimum distance d ≥ |{−1,0,…,15}|+1 = 18 (BCH-bound) [i]
- linear OA(711, 16, F7, 8) (dual of [16, 5, 9]-code), using contraction [i] based on linear OA(727, 32, F7, 17) (dual of [32, 5, 18]-code), using the narrow-sense BCH-code C(I) with length 32 | 74−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(712, 16, F7, 9) (dual of [16, 4, 10]-code), using contraction [i] based on linear OA(728, 32, F7, 19) (dual of [32, 4, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 32 | 74−1, defining interval I = [0,17], and minimum distance d ≥ |{−1,0,…,17}|+1 = 20 (BCH-bound) [i]
- linear OA(710, 16, F7, 7) (dual of [16, 6, 8]-code), using contraction [i] based on linear OA(726, 32, F7, 15) (dual of [32, 6, 16]-code), using the narrow-sense BCH-code C(I) with length 32 | 74−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code) (see above)
- construction XX applied to C1 = C([0,15]), C2 = C([1,17]), C3 = C1 + C2 = C([1,15]), and C∩ = C1 ∩ C2 = C([0,17]) [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.
Compare with Markus Grassl’s online database of code parameters.
Other Results with Identical Parameters
None.
Depending Results
None.