MinT - Information on Result #942132

Information on Result #942132

Linear OOA(4²⁵⁸, 201, F₄, 2, 107) (dual of [(201, 2), 144, 108]-NRT-code), using concatenation of two NRT-codes based on

linear OOA(16⁶², 67, F₁₆, 2, 53) (dual of [(67, 2), 72, 54]-NRT-code), using
- constructionÂ X applied to AG(2;F,74P) âŠ‚ AG(2;F,78P) [i] based on
  1. linear OOA(16⁵⁹, 64, F₁₆, 2, 53) (dual of [(64, 2), 69, 54]-NRT-code), using algebraic-geometric NRT-code AG(2;F,74P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]
  2. linear OOA(16⁵⁵, 64, F₁₆, 2, 49) (dual of [(64, 2), 73, 50]-NRT-code), using algebraic-geometric NRT-code AG(2;F,78P) [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65 (see above)
  3. linear OOA(16³, 3, F₁₆, 2, 3) (dual of [(3, 2), 3, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(16³, 16, F₁₆, 2, 3) (dual of [(16, 2), 29, 4]-NRT-code), using
      - Reedâ€“Solomon NRT-code RS(2;29,16) [i]
linear OA(4¹, 3, F₄, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
  - parity-check code [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(4²⁵⁸, 201, F₄, 2, 106) (dual of [(201, 2), 144, 107]-NRT-code)	[i]	Strength Reduction for OOAs
2	Linear OOA(4²⁶⁰, 202, F₄, 2, 107) (dual of [(202, 2), 144, 108]-NRT-code)	[i]	NRT-Code Embedding in Larger Space
3	Linear OOA(4²⁵⁹, 201, F₄, 2, 107) (dual of [(201, 2), 143, 108]-NRT-code)	[i]	OOA Duplication
4	Linear OOA(4²⁵⁷, 200, F₄, 2, 106) (dual of [(200, 2), 143, 107]-NRT-code)	[i]	Truncation for OOAs