Information on Result #1203443
Linear OOA(12878, 3495254, F128, 15, 12) (dual of [(3495254, 15), 52428732, 13]-NRT-code), using OOA 2-folding and stacking with additional row based on linear OOA(12878, 6990509, F128, 3, 12) (dual of [(6990509, 3), 20971449, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12878, 6990510, F128, 3, 12) (dual of [(6990510, 3), 20971452, 13]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- appending 2 arbitrary columns [i] based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 3, 1) for arbitrarily large s, using
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code) (see above)
- linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- Hamming code H(4,128) [i]
- appending kth column [i] based on linear OA(1284, 2113665, F128, 2) (dual of [2113665, 2113661, 3]-code), using
- appending 1 arbitrary column [i] based on linear OOA(1284, 2113665, F128, 2, 2) (dual of [(2113665, 2), 4227326, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 3, 2) (dual of [(2113665, 3), 6340991, 3]-NRT-code), using
- linear OOA(1284, 699051, F128, 3, 2) (dual of [(699051, 3), 2097149, 3]-NRT-code) (see above)
- linear OOA(1286, 699051, F128, 3, 3) (dual of [(699051, 3), 2097147, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1286, 2130049, F128, 3, 3) (dual of [(2130049, 3), 6390141, 4]-NRT-code), using
- linear OOA(12810, 699051, F128, 3, 4) (dual of [(699051, 3), 2097143, 5]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12810, 1048577, F128, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- linear OA(12810, 2097152, F128, 4) (dual of [2097152, 2097142, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(1287, 2097152, F128, 3) (dual of [2097152, 2097145, 4]-code or 2097152-cap in PG(6,128)), using an extension Ce(2) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,2], and designed minimum distance d ≥ |I|+1 = 3 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(2) [i] based on
- discarding factors / shortening the dual code based on linear OA(12810, 2097155, F128, 4) (dual of [2097155, 2097145, 5]-code), using
- OA 2-folding and stacking [i] based on linear OA(12810, 2097154, F128, 4) (dual of [2097154, 2097144, 5]-code), using
- discarding factors / shortening the dual code based on linear OOA(12810, 1048577, F128, 3, 4) (dual of [(1048577, 3), 3145721, 5]-NRT-code), using
- linear OOA(12816, 699051, F128, 3, 6) (dual of [(699051, 3), 2097137, 7]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- linear OA(12816, 2097152, F128, 6) (dual of [2097152, 2097136, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(12813, 2097152, F128, 5) (dual of [2097152, 2097139, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code) (see above)
- construction X applied to Ce(5) ⊂ Ce(4) [i] based on
- discarding factors / shortening the dual code based on linear OA(12816, 2097155, F128, 6) (dual of [2097155, 2097139, 7]-code), using
- OOA 3-folding [i] based on linear OA(12816, 2097153, F128, 6) (dual of [2097153, 2097137, 7]-code), using
- linear OOA(12834, 699051, F128, 3, 12) (dual of [(699051, 3), 2097119, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12834, 2097153, F128, 12) (dual of [2097153, 2097119, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(12834, 2097152, F128, 12) (dual of [2097152, 2097118, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code) (see above)
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- discarding factors / shortening the dual code based on linear OA(12834, 2097155, F128, 12) (dual of [2097155, 2097121, 13]-code), using
- OOA 3-folding [i] based on linear OA(12834, 2097153, F128, 12) (dual of [2097153, 2097119, 13]-code), using
- linear OOA(1281, 699051, F128, 3, 1) (dual of [(699051, 3), 2097152, 2]-NRT-code), using
- generalized (u, u+v)-construction [i] based on
Mode: Constructive and linear.
Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Digital (66, 78, 3495254)-net over F128 | [i] | Net Defined by OOA | |