MinT - Information on Result #1047872

Information on Result #1047872

Linear OOA(2²⁴³, 207, F₂, 3, 60) (dual of [(207, 3), 378, 61]-NRT-code), using trace code based on linear OOA(8⁸¹, 69, F₈, 3, 60) (dual of [(69, 3), 126, 61]-NRT-code), using

constructionÂ X applied to AG(3;F,131P) âŠ‚ AG(3;F,139P) [i] based on
1. linear OOA(8⁷⁴, 64, F₈, 3, 60) (dual of [(64, 3), 118, 61]-NRT-code), using algebraic-geometric NRT-code AG(3;F,131P) [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(8⁶⁶, 64, F₈, 3, 52) (dual of [(64, 3), 126, 53]-NRT-code), using algebraic-geometric NRT-code AG(3;F,139P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;17,8) [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(2²⁴⁶, 208, F₂, 3, 60) (dual of [(208, 3), 378, 61]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁴⁴, 207, F₂, 3, 60) (dual of [(207, 3), 377, 61]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴⁵, 207, F₂, 3, 60) (dual of [(207, 3), 376, 61]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁴³, 103, F₂, 5, 60) (dual of [(103, 5), 272, 61]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁴³, 103, F₂, 6, 60) (dual of [(103, 6), 375, 61]-NRT-code)	[i]	OOA Folding