MinT - Information on Result #2768053

Information on Result #2768053

Linear OOA(2²⁵⁶, 70, F₂, 4, 151) (dual of [(70, 4), 24, 152]-NRT-code), using strength reduction based on linear OOA(2²⁵⁶, 70, F₂, 4, 153) (dual of [(70, 4), 24, 154]-NRT-code), using

concatenation of two NRT-codes [i] based on
1. linear OA(64¹⁰, 14, F₆₄, 10) (dual of [14, 4, 11]-code or 14-arc in PG(9,64)), using
  - discarding factors / shortening the dual code based on linear OA(64¹⁰, 64, F₆₄, 10) (dual of [64, 54, 11]-code or 64-arc in PG(9,64)), using
    - Reedâ€“Solomon code RS(54,64) [i]
2. linear OOA(2¹⁴, 5, F₂, 4, 13) (dual of [(5, 4), 6, 14]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(4;F,6P) [i] based on function field F/F₂ with g(F) = 1 and N(F) ≥ 5, using
    - an explicitly constructive algebraic function field [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(2²⁵⁴, 69, F₂, 4, 149) (dual of [(69, 4), 22, 150]-NRT-code)	[i]		Truncation for OOAs
2	Linear OOA(2²⁵³, 69, F₂, 4, 148) (dual of [(69, 4), 23, 149]-NRT-code)	[i]		Truncation for OOAs