MinT - Information on Result #1664643

Information on Result #1664643

Linear OOA(2¹⁴⁶, 1677725, F₂, 6, 13) (dual of [(1677725, 6), 10066204, 14]-NRT-code), using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2¹⁴⁶, 1677725, F₂, 5, 13) (dual of [(1677725, 5), 8388479, 14]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁷, 5, F₂, 5, 6) (dual of [(5, 5), 18, 7]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(5;F,18P) [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(2¹³⁹, 1677720, F₂, 5, 13) (dual of [(1677720, 5), 8388461, 14]-NRT-code), using
  - OOA 5-folding [i] based on linear OA(2¹³⁹, 8388600, F₂, 13) (dual of [8388600, 8388461, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹³⁹, large, F₂, 13) (dual of [large, large−139, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [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(2¹⁴⁶, 1677724, F₂, 7, 13) (dual of [(1677724, 7), 11743922, 14]-NRT-code)	[i]		OOA Stacking with Additional Row
2	Linear OOA(2¹⁴⁶, 1677724, F₂, 8, 13) (dual of [(1677724, 8), 13421646, 14]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁶, 1677724, F₂, 18, 13) (dual of [(1677724, 18), 30198886, 14]-NRT-code)	[i]