MinT - Information on Result #940566

Information on Result #940566

Linear OOA(8¹⁵², 382, F₈, 2, 54) (dual of [(382, 2), 612, 55]-NRT-code), using trace code based on linear OOA(64⁷⁶, 191, F₆₄, 2, 54) (dual of [(191, 2), 306, 55]-NRT-code), using

constructionÂ X applied to AG(2;F,297P) âŠ‚ AG(2;F,313P) [i] based on
1. linear OOA(64⁶¹, 176, F₆₄, 2, 54) (dual of [(176, 2), 291, 55]-NRT-code), using algebraic-geometric NRT-code AG(2;F,297P) [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(64⁴⁵, 176, F₆₄, 2, 38) (dual of [(176, 2), 307, 39]-NRT-code), using algebraic-geometric NRT-code AG(2;F,313P) [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177 (see above)
3. linear OOA(64¹⁵, 15, F₆₄, 2, 15) (dual of [(15, 2), 15, 16]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(64¹⁵, 64, F₆₄, 2, 15) (dual of [(64, 2), 113, 16]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(2;113,64) [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(8¹⁵³, 382, F₈, 2, 54) (dual of [(382, 2), 611, 55]-NRT-code)	[i]		OOA Duplication
2	Linear OOA(8¹⁵², 191, F₈, 3, 54) (dual of [(191, 3), 421, 55]-NRT-code)	[i]		OOA Folding