MinT - Information on Result #941619

Information on Result #941619

Linear OOA(2²²⁹, 117, F₂, 2, 146) (dual of [(117, 2), 5, 147]-NRT-code), using juxtaposition based on

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
    1. 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]
    2. 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]
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) (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		This result only	Method
1	Linear OOA(2²²⁹, 117, F₂, 2, 145) (dual of [(117, 2), 5, 146]-NRT-code)	[i]		Strength Reduction for OOAs
2	Linear OOA(2²²⁹, 117, F₂, 2, 144) (dual of [(117, 2), 5, 145]-NRT-code)	[i]
3	Linear OOA(2²²⁹, 117, F₂, 2, 143) (dual of [(117, 2), 5, 144]-NRT-code)	[i]
4	Linear OOA(2²²⁹, 117, F₂, 2, 142) (dual of [(117, 2), 5, 143]-NRT-code)	[i]
5	Linear OOA(2²²⁹, 117, F₂, 2, 141) (dual of [(117, 2), 5, 142]-NRT-code)	[i]
6	Linear OOA(2²²⁹, 117, F₂, 2, 140) (dual of [(117, 2), 5, 141]-NRT-code)	[i]
7	Linear OOA(2²²⁸, 116, F₂, 2, 145) (dual of [(116, 2), 4, 146]-NRT-code)	[i]		Truncation for OOAs