Information on Result #896308
Linear OOA(768, 5764978, F7, 2, 8) (dual of [(5764978, 2), 11529888, 9]-NRT-code), using (u, u+v)-construction based on
- linear OOA(710, 174, F7, 2, 4) (dual of [(174, 2), 338, 5]-NRT-code), using
- OOA 2-folding [i] based on linear OA(710, 348, F7, 4) (dual of [348, 338, 5]-code), using
- construction XX applied to C1 = C([341,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([341,2]) [i] based on
- linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1}, and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(77, 342, F7, 3) (dual of [342, 335, 4]-code or 342-cap in PG(6,7)), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,2], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(710, 342, F7, 4) (dual of [342, 332, 5]-code), using the primitive BCH-code C(I) with length 342 = 73−1, defining interval I = {−1,0,1,2}, and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(74, 342, F7, 2) (dual of [342, 338, 3]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 342 = 73−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(70, 3, F7, 0) (dual of [3, 3, 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, 3, F7, 0) (dual of [3, 3, 1]-code) (see above)
- construction XX applied to C1 = C([341,1]), C2 = C([0,2]), C3 = C1 + C2 = C([0,1]), and C∩ = C1 ∩ C2 = C([341,2]) [i] based on
- OOA 2-folding [i] based on linear OA(710, 348, F7, 4) (dual of [348, 338, 5]-code), using
- linear OOA(758, 5764804, F7, 2, 8) (dual of [(5764804, 2), 11529550, 9]-NRT-code), using
- trace code [i] based on linear OOA(4929, 2882402, F49, 2, 8) (dual of [(2882402, 2), 5764775, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- linear OA(4929, 5764801, F49, 8) (dual of [5764801, 5764772, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(4925, 5764801, F49, 7) (dual of [5764801, 5764776, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(490, 4, F49, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(7) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(4929, 5764805, F49, 8) (dual of [5764805, 5764776, 9]-code), using
- OOA 2-folding [i] based on linear OA(4929, 5764804, F49, 8) (dual of [5764804, 5764775, 9]-code), using
- trace code [i] based on linear OOA(4929, 2882402, F49, 2, 8) (dual of [(2882402, 2), 5764775, 9]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and s, k and t, m and s, m and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(768, 2882489, F7, 3, 8) (dual of [(2882489, 3), 8647399, 9]-NRT-code) | [i] | OOA Folding | |
| 2 | Linear OOA(768, 2882488, F7, 10, 8) (dual of [(2882488, 10), 28824812, 9]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |