MinT - Information on Result #1047811

Information on Result #1047811

Linear OOA(2²⁰⁴, 204, F₂, 3, 48) (dual of [(204, 3), 408, 49]-NRT-code), using trace code based on linear OOA(8⁶⁸, 68, F₈, 3, 48) (dual of [(68, 3), 136, 49]-NRT-code), using

constructionÂ X applied to AG(3;F,143P) âŠ‚ AG(3;F,150P) [i] based on
1. linear OOA(8⁶², 64, F₈, 3, 48) (dual of [(64, 3), 130, 49]-NRT-code), using algebraic-geometric NRT-code AG(3;F,143P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
  - the Suzuki function field over F₈ [i]
2. linear OOA(8⁵⁵, 64, F₈, 3, 41) (dual of [(64, 3), 137, 42]-NRT-code), using algebraic-geometric NRT-code AG(3;F,150P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁶, 4, F₈, 3, 6) (dual of [(4, 3), 6, 7]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁶, 8, F₈, 3, 6) (dual of [(8, 3), 18, 7]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;18,8) [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(2²⁰⁵, 204, F₂, 3, 48) (dual of [(204, 3), 407, 49]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁰⁶, 204, F₂, 3, 48) (dual of [(204, 3), 406, 49]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁴, 102, F₂, 5, 48) (dual of [(102, 5), 306, 49]-NRT-code)	[i]	OOA Folding
4	Linear OOA(2²⁰⁴, 102, F₂, 6, 48) (dual of [(102, 6), 408, 49]-NRT-code)	[i]	OOA Folding