Information on Result #2694773
Linear OOA(5135, large, F5, 3, 10), using 1 times NRT-code embedding in larger space based on linear OOA(5132, 8388602, F5, 3, 10) (dual of [(8388602, 3), 25165674, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(540, 4194301, F5, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- the primitive narrow-sense BCH-code C(I) with length 9765624 = 510−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- OOA 2-folding and stacking with additional row [i] based on linear OA(540, large, F5, 5) (dual of [large, large−40, 6]-code), using
- linear OOA(592, 4194301, F5, 3, 10) (dual of [(4194301, 3), 12582811, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(592, 8388602, F5, 2, 10) (dual of [(8388602, 2), 16777112, 11]-NRT-code), using
- trace code [i] based on linear OOA(2546, 4194301, F25, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2546, 8388602, F25, 10) (dual of [8388602, 8388556, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 9765624 = 255−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2546, large, F25, 10) (dual of [large, large−46, 11]-code), using
- OOA 2-folding [i] based on linear OA(2546, 8388602, F25, 10) (dual of [8388602, 8388556, 11]-code), using
- trace code [i] based on linear OOA(2546, 4194301, F25, 2, 10) (dual of [(4194301, 2), 8388556, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(592, 8388602, F5, 2, 10) (dual of [(8388602, 2), 16777112, 11]-NRT-code), using
- linear OOA(540, 4194301, F5, 3, 5) (dual of [(4194301, 3), 12582863, 6]-NRT-code), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, k and t, 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(5137, large, F5, 3, 10) | [i] | OOA Duplication | |
| 2 | Linear OOA(5135, 4194301, F5, 15, 10) (dual of [(4194301, 15), 62914380, 11]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |