MinT - Information on Result #2627588

Information on Result #2627588

Linear OOA(3²²⁵, 93, F₃, 3, 122) (dual of [(93, 3), 54, 123]-NRT-code), using strength reduction based on linear OOA(3²²⁵, 93, F₃, 3, 123) (dual of [(93, 3), 54, 124]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OOA(9⁶⁶, 31, F₉, 3, 61) (dual of [(31, 3), 27, 62]-NRT-code), using
  - discarding factors / shortening the dual code based on linear OOA(9⁶⁶, 32, F₉, 3, 61) (dual of [(32, 3), 30, 62]-NRT-code), using
    - extended algebraic-geometric NRT-code AG_e(3;F,34P) [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
      - a function field by GarcÃa and Quoos [i]
2. linear OA(3¹, 3, F₃, 1) (dual of [3, 2, 2]-code), using
  - discarding factors / shortening the dual code based on linear OA(3¹, s, F₃, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
    - parity-check code [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(3²²⁶, 93, F₃, 3, 122) (dual of [(93, 3), 53, 123]-NRT-code)	[i]		OOA Duplication