MinT - Information on Result #2418139

Information on Result #2418139

Linear OOA(2⁹⁶, 63, F₂, 2, 40) (dual of [(63, 2), 30, 41]-NRT-code), using strength reduction based on linear OOA(2⁹⁶, 63, F₂, 2, 41) (dual of [(63, 2), 30, 42]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4²⁷, 21, F₄, 2, 20) (dual of [(21, 2), 15, 21]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,21P) [i] based on function field F/F₄ with g(F) = 7 and N(F) ≥ 21, 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(2⁹⁸, 64, F₂, 2, 40) (dual of [(64, 2), 30, 41]-NRT-code)	[i]		NRT-Code Embedding in Larger Space