Information on Result #1728188
Digital (105, 125, 449009)-net over F8, using net defined by OOA based on linear OOA(8125, 449009, F8, 27, 20) (dual of [(449009, 27), 12123118, 21]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(8125, 1796037, F8, 3, 20) (dual of [(1796037, 3), 5387986, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8125, 1796040, F8, 3, 20) (dual of [(1796040, 3), 5387995, 21]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8125, 1796040, F8, 20) (dual of [1796040, 1795915, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(8125, 2097179, F8, 20) (dual of [2097179, 2097054, 21]-code), using
- construction XX applied to Ce(19) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(8120, 2097152, F8, 20) (dual of [2097152, 2097032, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(899, 2097152, F8, 17) (dual of [2097152, 2097053, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(892, 2097152, F8, 15) (dual of [2097152, 2097060, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 87−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(83, 25, F8, 2) (dual of [25, 22, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 82−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(83, 63, F8, 2) (dual of [63, 60, 3]-code), using
- linear OA(81, 2, F8, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(19) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(8125, 2097179, F8, 20) (dual of [2097179, 2097054, 21]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(8125, 1796040, F8, 20) (dual of [1796040, 1795915, 21]-code), using
- discarding factors / shortening the dual code based on linear OOA(8125, 1796040, F8, 3, 20) (dual of [(1796040, 3), 5387995, 21]-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.