Information on Result #701337
Linear OA(723, 59, F7, 12) (dual of [59, 36, 13]-code), using construction XX applied to C1 = C({0,1,2,3,4,5,6,34,41}), C2 = C([1,9]), C3 = C1 + C2 = C([1,6]), and C∩ = C1 ∩ C2 = C({0,1,2,3,4,5,6,8,9,34,41}) based on
- linear OA(717, 48, F7, 10) (dual of [48, 31, 11]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,34,41}, and minimum distance d ≥ |{−2,−1,…,7}|+1 = 11 (BCH-bound) [i]
- linear OA(715, 48, F7, 9) (dual of [48, 33, 10]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(720, 48, F7, 12) (dual of [48, 28, 13]-code), using the primitive cyclic code C(A) with length 48 = 72−1, defining set A = {0,1,2,3,4,5,6,8,9,34,41}, and minimum distance d ≥ |{−2,−1,…,9}|+1 = 13 (BCH-bound) [i]
- linear OA(712, 48, F7, 7) (dual of [48, 36, 8]-code), using the primitive narrow-sense BCH-code C(I) with length 48 = 72−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(72, 7, F7, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,7)), using
- Reed–Solomon code RS(5,7) [i]
- linear OA(71, 4, F7, 1) (dual of [4, 3, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 2]-code), using
- Reed–Solomon code RS(6,7) [i]
- discarding factors / shortening the dual code based on linear OA(71, 7, F7, 1) (dual of [7, 6, 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.
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Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(723, 29, F7, 2, 12) (dual of [(29, 2), 35, 13]-NRT-code) | [i] | OOA Folding | |