MinT - Information on Result #2530097

Information on Result #2530097

Linear OOA(4²⁴⁴, 125, F₄, 2, 196) (dual of [(125, 2), 6, 197]-NRT-code), using strength reduction based on linear OOA(4²⁴⁴, 125, F₄, 2, 197) (dual of [(125, 2), 6, 198]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(16²², 25, F₁₆, 21) (dual of [25, 3, 22]-code), using
  - extended algebraic-geometric code AG_e(F,3P) [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 25, using
    - sharp bound on the number of rational points on curves with genus 1 [i]
2. linear OOA(4⁸, 5, F₄, 2, 8) (dual of [(5, 2), 2, 9]-NRT-code), using
  - extended Reedâ€“Solomon NRT-code RS_e(2;2,4) [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	Linear OOA(4²⁴⁶, 126, F₄, 2, 196) (dual of [(126, 2), 6, 197]-NRT-code)	[i]		NRT-Code Embedding in Larger Space
2	Linear OOA(4²⁴³, 124, F₄, 2, 195) (dual of [(124, 2), 5, 196]-NRT-code)	[i]		Truncation for OOAs
3	Linear OOA(4²⁴², 124, F₄, 2, 194) (dual of [(124, 2), 6, 195]-NRT-code)	[i]
4	Linear OOA(4²⁴⁰, 123, F₄, 2, 192) (dual of [(123, 2), 6, 193]-NRT-code)	[i]
5	Linear OOA(4²³⁸, 122, F₄, 2, 190) (dual of [(122, 2), 6, 191]-NRT-code)	[i]