MinT - Information on Result #2670322

Information on Result #2670322

Linear OOA(2¹⁰², 43, F₂, 3, 51) (dual of [(43, 3), 27, 52]-NRT-code), using 2¹ times duplication based on linear OOA(2¹⁰¹, 43, F₂, 3, 51) (dual of [(43, 3), 28, 52]-NRT-code), using

1 times NRT-code embedding in larger space [i] based on linear OOA(2⁹⁸, 42, F₂, 3, 51) (dual of [(42, 3), 28, 52]-NRT-code), using
- concatenation of two NRT-codes [i] based on
  1. linear OOA(4²⁸, 14, F₄, 3, 25) (dual of [(14, 3), 14, 26]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,16P) [i] based on function field F/F₄ with g(F) = 3 and N(F) ≥ 14, using
      - an explicitly constructive algebraic function field [i]
  2. linear OA(2¹, 3, F₂, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹, s, F₂, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [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(2²¹⁸, 78, F₂, 3, 102) (dual of [(78, 3), 16, 103]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(2²¹⁸, 78, F₂, 3, 103) (dual of [(78, 3), 16, 104]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs