Information on Result #1084886
Linear OOA(12861, 4194304, F128, 4, 11) (dual of [(4194304, 4), 16777155, 12]-NRT-code), using generalized (u, u+v)-construction based on
- linear OOA(1281, 524288, F128, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1281, s, F128, 4, 1) for arbitrarily large s, using
- appending 3 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, 4, 1) for arbitrarily large s, using
- linear OOA(1281, 524288, F128, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
- linear OOA(1281, 524288, F128, 4, 1) (dual of [(524288, 4), 2097151, 2]-NRT-code) (see above)
- linear OOA(1284, 524288, F128, 4, 2) (dual of [(524288, 4), 2097148, 3]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1284, 2113665, F128, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- appending 2 arbitrary columns [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 2 arbitrary columns [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, 4, 2) (dual of [(2113665, 4), 8454656, 3]-NRT-code), using
- linear OOA(1284, 524288, F128, 4, 2) (dual of [(524288, 4), 2097148, 3]-NRT-code) (see above)
- linear OOA(1286, 524288, F128, 4, 3) (dual of [(524288, 4), 2097146, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1286, 2130050, F128, 4, 3) (dual of [(2130050, 4), 8520194, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1286, 2130050, F128, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(1286, 2130050, F128, 4, 3) (dual of [(2130050, 4), 8520194, 4]-NRT-code), using
- linear OOA(12813, 524288, F128, 4, 5) (dual of [(524288, 4), 2097139, 6]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- construction X applied to Ce(4) ⊂ Ce(3) [i] based on
- 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(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(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(4) ⊂ Ce(3) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(12813, 2097155, F128, 5) (dual of [2097155, 2097142, 6]-code), using
- discarding factors / shortening the dual code based on linear OOA(12813, 1048577, F128, 4, 5) (dual of [(1048577, 4), 4194295, 6]-NRT-code), using
- linear OOA(12831, 524288, F128, 4, 11) (dual of [(524288, 4), 2097121, 12]-NRT-code), using
- OOA 4-folding [i] based on 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]
- OOA 4-folding [i] based on linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-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
None.