MinT - Information on Result #1683051

Information on Result #1683051

Linear OOA(2¹⁶⁹, 1677725, F₂, 7, 14) (dual of [(1677725, 7), 11743906, 15]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁶⁹, 1677725, F₂, 5, 14) (dual of [(1677725, 5), 8388456, 15]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁸, 5, F₂, 5, 7) (dual of [(5, 5), 17, 8]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,17P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [i]
2. linear OOA(2¹⁶¹, 1677720, F₂, 5, 14) (dual of [(1677720, 5), 8388439, 15]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹⁶¹, 8388600, F₂, 14) (dual of [8388600, 8388439, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁶¹, large, F₂, 14) (dual of [large, large−161, 15]-code), using
      - the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]

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

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(2¹⁶⁹, 1677724, F₂, 8, 14) (dual of [(1677724, 8), 13421623, 15]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁶⁹, 1677724, F₂, 21, 14) (dual of [(1677724, 21), 35232035, 15]-NRT-code)	[i]		OOA Stacking with Additional Row