MinT - Information on Result #2206522

Information on Result #2206522

Linear OA(4²²⁵, 270, F₄, 122) (dual of [270, 45, 123]-code), using strength reduction based on linear OA(4²²⁵, 270, F₄, 123) (dual of [270, 45, 124]-code), using

concatenation of two codes [i] based on
1. linear OA(64³⁰, 45, F₆₄, 30) (dual of [45, 15, 31]-code or 45-arc in PG(29,64)), using
  - discarding factors / shortening the dual code based on linear OA(64³⁰, 64, F₆₄, 30) (dual of [64, 34, 31]-code or 64-arc in PG(29,64)), using
    - Reedâ€“Solomon code RS(34,64) [i]
2. linear OA(4³, 6, F₄, 3) (dual of [6, 3, 4]-code or 6-arc in PG(2,4) or 6-cap in PG(2,4)), using
  - hyperoval in PG(2,Â 4) [i]
  - the Hexacode [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		Method
1	Linear OA(4²²⁴, 269, F₄, 121) (dual of [269, 45, 122]-code)	[i]	Truncation
2	Linear OA(4²²³, 268, F₄, 120) (dual of [268, 45, 121]-code)	[i]	Truncation
3	Linear OOA(4²²⁵, 135, F₄, 2, 122) (dual of [(135, 2), 45, 123]-NRT-code)	[i]	OOA Folding
4	Linear OOA(4²²⁵, 90, F₄, 3, 122) (dual of [(90, 3), 45, 123]-NRT-code)	[i]	OOA Folding