MinT - Information on Result #941589

Information on Result #941589

Linear OOA(2²²¹, 113, F₂, 2, 140) (dual of [(113, 2), 5, 141]-NRT-code), using juxtaposition based on

linear OOA(2⁵, 5, F₂, 2, 4) (dual of [(5, 2), 5, 5]-NRT-code), using
- extended algebraic-geometric NRT-code AG_e(2;F,5P) [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(2²¹¹, 108, F₂, 2, 135) (dual of [(108, 2), 5, 136]-NRT-code), using
- 2 step truncation [i] based on linear OOA(2²¹³, 109, F₂, 2, 137) (dual of [(109, 2), 5, 138]-NRT-code), using
  - juxtaposition [i] based on
    1. linear OOA(2⁸⁹, 47, F₂, 2, 58) (dual of [(47, 2), 5, 59]-NRT-code), using
      - 1 step truncation [i] based on linear OOA(2⁹⁰, 48, F₂, 2, 59) (dual of [(48, 2), 6, 60]-NRT-code), using
        concatenation of two NRT-codes [i] based on
        linear OA(4¹³, 16, F₄, 11) (dual of [16, 3, 12]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹³, 17, F₄, 11) (dual of [17, 4, 12]-code), using
        projective code from ovoid in PG(3,Â 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]
    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) (see above)

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(2²²¹, 113, F₂, 2, 139) (dual of [(113, 2), 5, 140]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(2²²¹, 113, F₂, 2, 138) (dual of [(113, 2), 5, 139]-NRT-code)	[i]
3	Linear OOA(2²²¹, 113, F₂, 2, 137) (dual of [(113, 2), 5, 138]-NRT-code)	[i]
4	Linear OOA(2²²¹, 113, F₂, 2, 136) (dual of [(113, 2), 5, 137]-NRT-code)	[i]
5	Linear OOA(2²²¹, 113, F₂, 2, 135) (dual of [(113, 2), 5, 136]-NRT-code)	[i]