MinT - Information on Result #940319

Information on Result #940319

Linear OOA(8¹⁰², 360, F₈, 2, 40) (dual of [(360, 2), 618, 41]-NRT-code), using trace code based on linear OOA(64⁵¹, 180, F₆₄, 2, 40) (dual of [(180, 2), 309, 41]-NRT-code), using

constructionÂ X applied to AG(2;F,311P) âŠ‚ AG(2;F,316P) [i] based on
1. linear OOA(64⁴⁷, 176, F₆₄, 2, 40) (dual of [(176, 2), 305, 41]-NRT-code), using algebraic-geometric NRT-code AG(2;F,311P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
  - a function field by GarcÃa and Quoos [i]
2. linear OOA(64⁴², 176, F₆₄, 2, 35) (dual of [(176, 2), 310, 36]-NRT-code), using algebraic-geometric NRT-code AG(2;F,316P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64⁴, 4, F₆₄, 2, 4) (dual of [(4, 2), 4, 5]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64⁴, 64, F₆₄, 2, 4) (dual of [(64, 2), 124, 5]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;124,64) [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		This result only	Method
1	Linear OOA(8¹⁰³, 360, F₈, 2, 40) (dual of [(360, 2), 617, 41]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁰², 180, F₈, 3, 40) (dual of [(180, 3), 438, 41]-NRT-code)	[i]		OOA Folding