MinT - Information on Result #941617

Information on Result #941617

Linear OOA(2²²³, 114, F₂, 2, 142) (dual of [(114, 2), 5, 143]-NRT-code), using juxtaposition based on

linear OOA(2⁸³, 44, F₂, 2, 54) (dual of [(44, 2), 5, 55]-NRT-code), using
- 1 step truncation [i] based on linear OOA(2⁸⁴, 45, F₂, 2, 55) (dual of [(45, 2), 6, 56]-NRT-code), using
  - concatenation of two NRT-codes [i] based on
    1. linear OA(8⁷, 9, F₈, 7) (dual of [9, 2, 8]-code or 9-arc in PG(6,8)), using
      - extended Reedâ€“Solomon code RS_e(2,8) [i]
      - Simplex code S(2,8) [i]
    2. linear OOA(2⁷, 5, F₂, 2, 6) (dual of [(5, 2), 3, 7]-NRT-code), using
      - extended algebraic-geometric NRT-code AG_e(2;F,3P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
        an explicitly constructive algebraic function field [i]
linear OOA(2¹³⁵, 70, F₂, 2, 87) (dual of [(70, 2), 5, 88]-NRT-code), using
- juxtaposition [i] based on
  1. linear OOA(2¹¹, 8, F₂, 2, 8) (dual of [(8, 2), 5, 9]-NRT-code), using
    - an explicit generator matrix by Edel [i]
  2. linear OOA(2¹¹⁹, 62, F₂, 2, 78) (dual of [(62, 2), 5, 79]-NRT-code), using
    - 1 step truncation [i] based on linear OOA(2¹²⁰, 63, F₂, 2, 79) (dual of [(63, 2), 6, 80]-NRT-code), using
      - concatenation of two NRT-codes [i] based on
        linear OA(4¹⁸, 21, F₄, 15) (dual of [21, 3, 16]-code), using
        Simplex code S(3,4) [i]
        linear OOA(2⁴, 3, F₂, 2, 4) (dual of [(3, 2), 2, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;2,2) [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		This result only	Method
1	Linear OOA(2²¹⁹, 112, F₂, 2, 138) (dual of [(112, 2), 5, 139]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(2²¹⁷, 111, F₂, 2, 136) (dual of [(111, 2), 5, 137]-NRT-code)	[i]		Truncation for OOAs
3	Linear OOA(2²²³, 57, F₂, 4, 142) (dual of [(57, 4), 5, 143]-NRT-code)	[i]		OOA Folding