MinT - Information on Result #2458057

Information on Result #2458057

Linear OOA(2¹⁵⁰, 83, F₂, 2, 78) (dual of [(83, 2), 16, 79]-NRT-code), using 4 step truncation based on linear OOA(2¹⁵⁴, 85, F₂, 2, 82) (dual of [(85, 2), 16, 83]-NRT-code), using

strength reduction [i] based on linear OOA(2¹⁵⁴, 85, F₂, 2, 83) (dual of [(85, 2), 16, 84]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OA(16¹³, 17, F₁₆, 13) (dual of [17, 4, 14]-code or 17-arc in PG(12,16)), using
    - extended Reedâ€“Solomon code RS_e(4,16) [i]
    - the expurgated narrow-sense BCH-code C(I) with length 17Â | 16²âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]
  2. linear OOA(2⁶, 5, F₂, 2, 5) (dual of [(5, 2), 4, 6]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(2;F,4P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
      - an explicitly constructive algebraic function field [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁵⁶, 86, F₂, 2, 78) (dual of [(86, 2), 16, 79]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2¹⁵⁸, 87, F₂, 2, 78) (dual of [(87, 2), 16, 79]-NRT-code)	[i]
3	Linear OOA(2¹⁶⁰, 88, F₂, 2, 78) (dual of [(88, 2), 16, 79]-NRT-code)	[i]
4	Linear OOA(2²²², 115, F₂, 2, 114) (dual of [(115, 2), 8, 115]-NRT-code)	[i]	Juxtaposition for OOAs