Information on Result #1705942
Linear OOA(2246, 1677904, F2, 8, 19) (dual of [(1677904, 8), 13422986, 20]-NRT-code), using embedding of OOA with Gilbert–Varšamov bound based on linear OOA(2246, 1677904, F2, 5, 19) (dual of [(1677904, 5), 8389274, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(238, 184, F2, 5, 9) (dual of [(184, 5), 882, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 184, F2, 2, 9) (dual of [(184, 2), 330, 10]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(238, 261, F2, 2, 9) (dual of [(261, 2), 484, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(238, 522, F2, 9) (dual of [522, 484, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(228, 512, F2, 7) (dual of [512, 484, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(21, 10, F2, 1) (dual of [10, 9, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- OOA 2-folding [i] based on linear OA(238, 522, F2, 9) (dual of [522, 484, 10]-code), using
- discarding factors / shortening the dual code based on linear OOA(238, 261, F2, 2, 9) (dual of [(261, 2), 484, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 184, F2, 2, 9) (dual of [(184, 2), 330, 10]-NRT-code), using
- linear OOA(2208, 1677720, F2, 5, 19) (dual of [(1677720, 5), 8388392, 20]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 5-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- linear OOA(238, 184, F2, 5, 9) (dual of [(184, 5), 882, 10]-NRT-code), using
Mode: 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.