Information on Result #1709980
Digital (62, 79, 253)-net over F2, using net defined by OOA based on linear OOA(279, 253, F2, 24, 17) (dual of [(253, 24), 5993, 18]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(279, 254, F2, 8, 17) (dual of [(254, 8), 1953, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(279, 254, F2, 2, 17) (dual of [(254, 2), 429, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(279, 268, F2, 2, 17) (dual of [(268, 2), 457, 18]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(277, 267, F2, 2, 17) (dual of [(267, 2), 457, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(277, 534, F2, 17) (dual of [534, 457, 18]-code), using
- 1 times code embedding in larger space [i] based on linear OA(276, 533, F2, 17) (dual of [533, 457, 18]-code), using
- adding a parity check bit [i] based on linear OA(275, 532, F2, 16) (dual of [532, 457, 17]-code), using
- construction XX applied to C1 = C([509,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([509,14]) [i] based on
- linear OA(264, 511, F2, 15) (dual of [511, 447, 16]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,12}, and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(273, 511, F2, 17) (dual of [511, 438, 18]-code), using the primitive BCH-code C(I) with length 511 = 29−1, defining interval I = {−2,−1,…,14}, and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(254, 511, F2, 12) (dual of [511, 457, 13]-code), using the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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, 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 (see above)
- construction XX applied to C1 = C([509,12]), C2 = C([1,14]), C3 = C1 + C2 = C([1,12]), and C∩ = C1 ∩ C2 = C([509,14]) [i] based on
- adding a parity check bit [i] based on linear OA(275, 532, F2, 16) (dual of [532, 457, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(276, 533, F2, 17) (dual of [533, 457, 18]-code), using
- OOA 2-folding [i] based on linear OA(277, 534, F2, 17) (dual of [534, 457, 18]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(277, 267, F2, 2, 17) (dual of [(267, 2), 457, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(279, 268, F2, 2, 17) (dual of [(268, 2), 457, 18]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(279, 254, F2, 2, 17) (dual of [(254, 2), 429, 18]-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.