Information on Result #737733
Linear OA(7110, 823595, F7, 17) (dual of [823595, 823485, 18]-code), using construction X applied to Ce(16) ⊂ Ce(9) based on
- linear OA(799, 823543, F7, 17) (dual of [823543, 823444, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(757, 823543, F7, 10) (dual of [823543, 823486, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(711, 52, F7, 6) (dual of [52, 41, 7]-code), using
- construction XX applied to C1 = C({0,1,2,3,41}), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,41}) [i] based on
- linear OA(79, 48, F7, 5) (dual of [48, 39, 6]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,41}, and minimum distance d ≥ |{−1,0,1,2,3}|+1 = 6 (BCH-bound) [i]
- linear OA(79, 48, F7, 5) (dual of [48, 39, 6]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,4], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(711, 48, F7, 6) (dual of [48, 37, 7]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,41}, and minimum distance d ≥ |{−1,0,…,4}|+1 = 7 (BCH-bound) [i]
- linear OA(77, 48, F7, 4) (dual of [48, 41, 5]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- linear OA(70, 2, F7, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C({0,1,2,3,41}), C2 = C([0,4]), C3 = C1 + C2 = C([0,3]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,41}) [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
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(7110, 823595, F7, 2, 17) (dual of [(823595, 2), 1647080, 18]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(7110, 823595, F7, 3, 17) (dual of [(823595, 3), 2470675, 18]-NRT-code) | [i] | ||
| 3 | Digital (93, 110, 823595)-net over F7 | [i] | ||
| 4 | Linear OOA(7110, 411797, F7, 2, 17) (dual of [(411797, 2), 823484, 18]-NRT-code) | [i] | OOA Folding | |