MinT - Information on Result #2417623

Information on Result #2417623

Linear OOA(2⁸⁰, 42, F₂, 2, 53) (dual of [(42, 2), 4, 54]-NRT-code), using strength reduction based on linear OOA(2⁸⁰, 42, F₂, 2, 54) (dual of [(42, 2), 4, 55]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(4¹², 14, F₄, 10) (dual of [14, 2, 11]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹², 16, F₄, 10) (dual of [16, 4, 11]-code), using
    - 1 times truncation [i] 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]

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(2⁸⁰, 21, F₂, 4, 53) (dual of [(21, 4), 4, 54]-NRT-code)	[i]		OOA Folding