MinT - Information on Result #2670983

Information on Result #2670983

Linear OOA(2²⁴³, 214, F₂, 3, 56) (dual of [(214, 3), 399, 57]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2²⁴⁰, 213, F₂, 3, 56) (dual of [(213, 3), 399, 57]-NRT-code), using

trace code [i] based on linear OOA(8⁸⁰, 71, F₈, 3, 56) (dual of [(71, 3), 133, 57]-NRT-code), using
- constructionÂ X applied to AG(3;F,135P) âŠ‚ AG(3;F,146P) [i] based on
  1. linear OOA(8⁷⁰, 64, F₈, 3, 56) (dual of [(64, 3), 122, 57]-NRT-code), using algebraic-geometric NRT-code AG(3;F,135P) [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(8⁵⁹, 64, F₈, 3, 45) (dual of [(64, 3), 133, 46]-NRT-code), using algebraic-geometric NRT-code AG(3;F,146P) [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(2²⁴⁴, 214, F₂, 3, 56) (dual of [(214, 3), 398, 57]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2²⁴⁵, 214, F₂, 3, 56) (dual of [(214, 3), 397, 57]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2²⁴³, 107, F₂, 6, 56) (dual of [(107, 6), 399, 57]-NRT-code)	[i]	OOA Folding