Information on Result #1707660
Digital (27, 36, 137)-net over F2, using net defined by OOA based on linear OOA(236, 137, F2, 9, 9) (dual of [(137, 9), 1197, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(236, 137, F2, 8, 9) (dual of [(137, 8), 1060, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 137, F2, 2, 9) (dual of [(137, 2), 238, 10]-NRT-code), using
- OOA 2-folding [i] based on linear OA(236, 274, F2, 9) (dual of [274, 238, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(236, 275, F2, 9) (dual of [275, 239, 10]-code), using
- adding a parity check bit [i] based on linear OA(235, 274, F2, 8) (dual of [274, 239, 9]-code), using
- construction XX applied to C1 = C([253,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- linear OA(225, 255, F2, 7) (dual of [255, 230, 8]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,4}, and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(224, 255, F2, 6) (dual of [255, 231, 7]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(233, 255, F2, 9) (dual of [255, 222, 10]-code), using the primitive BCH-code C(I) with length 255 = 28−1, defining interval I = {−2,−1,…,6}, and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(216, 255, F2, 4) (dual of [255, 239, 5]-code), using the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [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
- linear OA(21, 9, F2, 1) (dual of [9, 8, 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 (see above)
- construction XX applied to C1 = C([253,4]), C2 = C([1,6]), C3 = C1 + C2 = C([1,4]), and C∩ = C1 ∩ C2 = C([253,6]) [i] based on
- adding a parity check bit [i] based on linear OA(235, 274, F2, 8) (dual of [274, 239, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(236, 275, F2, 9) (dual of [275, 239, 10]-code), using
- OOA 2-folding [i] based on linear OA(236, 274, F2, 9) (dual of [274, 238, 10]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 137, F2, 2, 9) (dual of [(137, 2), 238, 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, t and s.
Other Results with Identical Parameters
None.
Depending Results
None.