Information on Result #701342
Linear OA(718, 52, F7, 11) (dual of [52, 34, 12]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,8,41}), C2 = C([0,9]), C3 = C1 + C2 = C([0,8]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,41}) based on
- linear OA(716, 48, F7, 10) (dual of [48, 32, 11]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,41}, and minimum distance d ≥ |{−1,0,…,8}|+1 = 11 (BCH-bound) [i]
- linear OA(716, 48, F7, 10) (dual of [48, 32, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(718, 48, F7, 11) (dual of [48, 30, 12]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,41}, and minimum distance d ≥ |{−1,0,…,9}|+1 = 12 (BCH-bound) [i]
- linear OA(714, 48, F7, 9) (dual of [48, 34, 10]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [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)
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:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(718, 26, F7, 2, 11) (dual of [(26, 2), 34, 12]-NRT-code) | [i] | OOA Folding | |