MinT - Information on Result #2720620

Information on Result #2720620

Linear OOA(8¹¹⁵, 148, F₈, 3, 62) (dual of [(148, 3), 329, 63]-NRT-code), using strength reduction based on linear OOA(8¹¹⁵, 148, F₈, 3, 63) (dual of [(148, 3), 329, 64]-NRT-code), using

constructionÂ X applied to AG(3;F,365P) âŠ‚ AG(3;F,373P) [i] based on
1. linear OOA(8¹⁰⁸, 143, F₈, 3, 63) (dual of [(143, 3), 321, 64]-NRT-code), using algebraic-geometric NRT-code AG(3;F,365P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
  - Drinfeld modules of rank 1 [i]
2. linear OOA(8¹⁰⁰, 143, F₈, 3, 55) (dual of [(143, 3), 329, 56]-NRT-code), using algebraic-geometric NRT-code AG(3;F,373P) [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144 (see above)
3. linear OOA(8⁷, 5, F₈, 3, 7) (dual of [(5, 3), 8, 8]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(8⁷, 8, F₈, 3, 7) (dual of [(8, 3), 17, 8]-NRT-code), using
    - Reedâ€“Solomon NRT-code RS(3;17,8) [i]

Mode: 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	Digital (53, 115, 145)-net over F₈	[i]		Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound