MinT - Information on Result #1047816

Information on Result #1047816

Linear OOA(2²⁰⁷, 201, F₂, 3, 51) (dual of [(201, 3), 396, 52]-NRT-code), using trace code based on linear OOA(8⁶⁹, 67, F₈, 3, 51) (dual of [(67, 3), 132, 52]-NRT-code), using

constructionÂ X applied to AG(3;F,140P) âŠ‚ AG(3;F,145P) [i] based on
1. linear OOA(8⁶⁵, 64, F₈, 3, 51) (dual of [(64, 3), 127, 52]-NRT-code), using algebraic-geometric NRT-code AG(3;F,140P) [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(8⁶⁰, 64, F₈, 3, 46) (dual of [(64, 3), 132, 47]-NRT-code), using algebraic-geometric NRT-code AG(3;F,145P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁴, 3, F₈, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁴, 8, F₈, 3, 4) (dual of [(8, 3), 20, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;20,8) [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(2²¹⁰, 202, F₂, 3, 51) (dual of [(202, 3), 396, 52]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁰⁸, 201, F₂, 3, 51) (dual of [(201, 3), 395, 52]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁰⁹, 201, F₂, 3, 51) (dual of [(201, 3), 394, 52]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁰⁷, 100, F₂, 5, 51) (dual of [(100, 5), 293, 52]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁰⁷, 100, F₂, 6, 51) (dual of [(100, 6), 393, 52]-NRT-code)	[i]	OOA Folding