Information on Result #685935
Linear OA(756, 72, F7, 34) (dual of [72, 16, 35]-code), using construction XX applied to C1 = C([0,47]), C2 = C([1,67]), C3 = C1 + C2 = C([1,47]), and C∩ = C1 ∩ C2 = C([0,67]) based on
- linear OA(733, 48, F7, 24) (dual of [48, 15, 25]-code), using contraction [i] based on linear OA(781, 96, F7, 49) (dual of [96, 15, 50]-code), using the expurgated narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [0,47], and minimum distance d ≥ |{−1,0,…,47}|+1 = 50 (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(732, 48, F7, 23) (dual of [48, 16, 24]-code), using contraction [i] based on linear OA(780, 96, F7, 47) (dual of [96, 16, 48]-code), using the narrow-sense BCH-code C(I) with length 96 | 74−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- linear OA(70, 1, F7, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- linear OA(713, 23, F7, 9) (dual of [23, 10, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(713, 29, F7, 9) (dual of [29, 16, 10]-code), using
- 3 times truncation [i] based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- extended quadratic residue code Qe(32,7) [i]
- 3 times truncation [i] based on linear OA(716, 32, F7, 12) (dual of [32, 16, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(713, 29, F7, 9) (dual of [29, 16, 10]-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.
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(756, 24, F7, 3, 34) (dual of [(24, 3), 16, 35]-NRT-code) | [i] | OOA Folding | |