Information on Result #685983
Linear OA(718, 26, F7, 13) (dual of [26, 8, 14]-code), using construction XX applied to C1 = C([0,35]), C2 = C([1,38]), C3 = C1 + C2 = C([1,35]), and C∩ = C1 ∩ C2 = C([0,38]) based on
- linear OA(717, 24, F7, 12) (dual of [24, 7, 13]-code), using contraction [i] based on linear OA(765, 72, F7, 38) (dual of [72, 7, 39]-code), using the expurgated narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [0,35], and minimum distance d ≥ |{−2,−1,…,35}|+1 = 39 (BCH-bound) [i]
- linear OA(717, 24, F7, 12) (dual of [24, 7, 13]-code), using contraction [i] based on linear OA(765, 72, F7, 38) (dual of [72, 7, 39]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(718, 24, F7, 13) (dual of [24, 6, 14]-code), using contraction [i] based on linear OA(766, 72, F7, 41) (dual of [72, 6, 42]-code), using the expurgated narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [0,38], and minimum distance d ≥ |{−2,−1,…,38}|+1 = 42 (BCH-bound) [i]
- linear OA(716, 24, F7, 11) (dual of [24, 8, 12]-code), using contraction [i] based on linear OA(764, 72, F7, 35) (dual of [72, 8, 36]-code), using the narrow-sense BCH-code C(I) with length 72 | 76−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [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, 1, F7, 0) (dual of [1, 1, 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 OA(767, 76, F7, 47) (dual of [76, 9, 48]-code) | [i] | Construction X with Cyclic Codes | |
| 2 | Linear OA(769, 80, F7, 45) (dual of [80, 11, 46]-code) | [i] | Construction XX with Cyclic Codes | |
| 3 | Linear OOA(718, 13, F7, 2, 13) (dual of [(13, 2), 8, 14]-NRT-code) | [i] | OOA Folding | |