MinT - Information on Result #2616444

Information on Result #2616444

Linear OOA(2²⁰⁶, 90, F₂, 3, 90) (dual of [(90, 3), 64, 91]-NRT-code), using strength reduction based on linear OOA(2²⁰⁶, 90, F₂, 3, 91) (dual of [(90, 3), 64, 92]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(4⁵⁸, 30, F₄, 3, 45) (dual of [(30, 3), 32, 46]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(3;F,44P) [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [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		Method
1	Linear OOA(2²⁰⁹, 91, F₂, 3, 90) (dual of [(91, 3), 64, 91]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰⁷, 90, F₂, 3, 90) (dual of [(90, 3), 63, 91]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁶, 45, F₂, 5, 90) (dual of [(45, 5), 19, 91]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2²⁰⁶, 45, F₂, 6, 90) (dual of [(45, 6), 64, 91]-NRT-code)	[i]	OOA Folding