MinT - Information on Result #1048568

Information on Result #1048568

Linear OOA(4²⁵², 555, F₄, 3, 64) (dual of [(555, 3), 1413, 65]-NRT-code), using trace code based on linear OOA(64⁸⁴, 185, F₆₄, 3, 64) (dual of [(185, 3), 471, 65]-NRT-code), using

constructionÂ X applied to AG(3;F,463P) âŠ‚ AG(3;F,477P) [i] based on
1. linear OOA(64⁷¹, 176, F₆₄, 3, 64) (dual of [(176, 3), 457, 65]-NRT-code), using algebraic-geometric NRT-code AG(3;F,463P) [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(64⁵⁷, 176, F₆₄, 3, 50) (dual of [(176, 3), 471, 51]-NRT-code), using algebraic-geometric NRT-code AG(3;F,477P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹³, 9, F₆₄, 3, 13) (dual of [(9, 3), 14, 14]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹³, 64, F₆₄, 3, 13) (dual of [(64, 3), 179, 14]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;179,64) [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(4²⁵³, 555, F₄, 3, 64) (dual of [(555, 3), 1412, 65]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(4²⁵⁴, 555, F₄, 3, 64) (dual of [(555, 3), 1411, 65]-NRT-code)	[i]		OOA Duplication