MinT - Information on Result #2657440

Information on Result #2657440

Linear OOA(2²²⁰, 98, F₂, 3, 92) (dual of [(98, 3), 74, 93]-NRT-code), using 1 step truncation based on linear OOA(2²²¹, 99, F₂, 3, 93) (dual of [(99, 3), 76, 94]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁶¹, 33, F₄, 3, 46) (dual of [(33, 3), 38, 47]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,52P) [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, 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(2²²⁰, 49, F₂, 5, 92) (dual of [(49, 5), 25, 93]-NRT-code)	[i]		OOA Folding
2	Linear OOA(2²²⁰, 49, F₂, 6, 92) (dual of [(49, 6), 74, 93]-NRT-code)	[i]		OOA Folding