Information on Result #1022682
Linear OOA(12878, 6990510, F128, 3, 12) (dual of [(6990510, 3), 20971452, 13]-NRT-code), using generalized (u, u+v)-construction 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
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(12878, 3495254, F128, 15, 12) (dual of [(3495254, 15), 52428732, 13]-NRT-code) | [i] | OOA Folding and Stacking with Additional Row | |