MinT - Information on Result #1047888

Information on Result #1047888

Linear OOA(2²⁵², 213, F₂, 3, 60) (dual of [(213, 3), 387, 61]-NRT-code), using trace code based on linear OOA(8⁸⁴, 71, F₈, 3, 60) (dual of [(71, 3), 129, 61]-NRT-code), using

constructionÂ X applied to AG(3;F,131P) âŠ‚ AG(3;F,142P) [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(8⁶³, 64, F₈, 3, 49) (dual of [(64, 3), 129, 50]-NRT-code), using algebraic-geometric NRT-code AG(3;F,142P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65 (see above)
3. linear OOA(8¹⁰, 7, F₈, 3, 10) (dual of [(7, 3), 11, 11]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8¹⁰, 8, F₈, 3, 10) (dual of [(8, 3), 14, 11]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;14,8) [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(2²⁵⁵, 214, F₂, 3, 60) (dual of [(214, 3), 387, 61]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
2	Linear OOA(2²⁵³, 213, F₂, 3, 60) (dual of [(213, 3), 386, 61]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁵⁴, 213, F₂, 3, 60) (dual of [(213, 3), 385, 61]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(2²⁵², 106, F₂, 5, 60) (dual of [(106, 5), 278, 61]-NRT-code)	[i]	OOA Folding
5	Linear OOA(2²⁵², 106, F₂, 6, 60) (dual of [(106, 6), 384, 61]-NRT-code)	[i]	OOA Folding