MinT - Information on Result #2669414

Information on Result #2669414

Linear OOA(2¹⁸³, 202, F₂, 3, 42) (dual of [(202, 3), 423, 43]-NRT-code), using 1 times NRT-code embedding in larger space based on linear OOA(2¹⁸⁰, 201, F₂, 3, 42) (dual of [(201, 3), 423, 43]-NRT-code), using

trace code [i] based on linear OOA(8⁶⁰, 67, F₈, 3, 42) (dual of [(67, 3), 141, 43]-NRT-code), using
- constructionÂ X applied to AG(3;F,149P) âŠ‚ AG(3;F,154P) [i] based on
  1. linear OOA(8⁵⁶, 64, F₈, 3, 42) (dual of [(64, 3), 136, 43]-NRT-code), using algebraic-geometric NRT-code AG(3;F,149P) [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(8⁵¹, 64, F₈, 3, 37) (dual of [(64, 3), 141, 38]-NRT-code), using algebraic-geometric NRT-code AG(3;F,154P) [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(2¹⁸⁴, 202, F₂, 3, 42) (dual of [(202, 3), 422, 43]-NRT-code)	[i]	OOA Duplication
2	Linear OOA(2¹⁸⁵, 202, F₂, 3, 42) (dual of [(202, 3), 421, 43]-NRT-code)	[i]	OOA Duplication
3	Linear OOA(2¹⁸³, 101, F₂, 6, 42) (dual of [(101, 6), 423, 43]-NRT-code)	[i]	OOA Folding