Information on Result #685939
Linear OA(743, 51, F7, 34) (dual of [51, 8, 35]-code), using construction XX applied to C1 = C([0,65]), C2 = C([1,67]), C3 = C1 + C2 = C([1,65]), and C∩ = C1 ∩ C2 = C([0,67]) based on
- linear OA(741, 48, F7, 33) (dual of [48, 7, 34]-code), using contraction [i] based on linear OA(789, 96, F7, 67) (dual of [96, 7, 68]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,65], and minimum distance d ≥ |{−1,0,…,65}|+1 = 68 (BCH-bound) [i]
- linear OA(742, 48, F7, 33) (dual of [48, 6, 34]-code), using contraction [i] based on linear OA(790, 96, F7, 67) (dual of [96, 6, 68]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,67], and designed minimum distance d ≥ |I|+1 = 68 [i]
- linear OA(743, 48, F7, 34) (dual of [48, 5, 35]-code), using contraction [i] based on linear OA(791, 96, F7, 69) (dual of [96, 5, 70]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,67], and minimum distance d ≥ |{−1,0,…,67}|+1 = 70 (BCH-bound) [i]
- linear OA(740, 48, F7, 32) (dual of [48, 8, 33]-code), using contraction [i] based on linear OA(788, 96, F7, 65) (dual of [96, 8, 66]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,65], and designed minimum distance d ≥ |I|+1 = 66 [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, 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
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(743, 17, F7, 3, 34) (dual of [(17, 3), 8, 35]-NRT-code) | [i] | OOA Folding | |