MinT - Information on Result #661527

Information on Result #661527

Linear OA(4²⁵³, 424, F₄, 91) (dual of [424, 171, 92]-code), using concatenation of two codes based on

linear OA(64⁴⁹, 106, F₆₄, 45) (dual of [106, 57, 46]-code), using
- constructionÂ X applied to AG(F,57P) âŠ‚ AG(F,59P) [i] based on
  1. linear OA(64⁴⁸, 103, F₆₄, 45) (dual of [103, 55, 46]-code), using algebraic-geometric code AG(F,57P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]
  2. linear OA(64⁴⁶, 103, F₆₄, 43) (dual of [103, 57, 44]-code), using algebraic-geometric code AG(F,59P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104 (see above)
  3. linear OA(64¹, 3, F₆₄, 1) (dual of [3, 2, 2]-code), using
    - discarding factors / shortening the dual code based on linear OA(64¹, s, F₆₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
      - parity-check code [i]
linear OA(4¹, 4, F₄, 1) (dual of [4, 3, 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 OA(4²⁵³, 424, F₄, 90) (dual of [424, 171, 91]-code)	[i]	Strength Reduction
2	Linear OA(4²⁵⁴, 425, F₄, 91) (dual of [425, 171, 92]-code)	[i]	Code Embedding in Larger Space
3	Linear OA(4²⁵⁵, 426, F₄, 91) (dual of [426, 171, 92]-code)	[i]
4	Linear OA(4²⁵⁶, 427, F₄, 91) (dual of [427, 171, 92]-code)	[i]
5	Linear OA(4²⁵², 423, F₄, 90) (dual of [423, 171, 91]-code)	[i]	Truncation
6	Linear OOA(4²⁵³, 212, F₄, 2, 91) (dual of [(212, 2), 171, 92]-NRT-code)	[i]	OOA Folding
7	Linear OOA(4²⁵³, 141, F₄, 3, 91) (dual of [(141, 3), 170, 92]-NRT-code)	[i]	OOA Folding