MinT - Information on Result #1300120

Information on Result #1300120

Linear OA(4¹²², 150, F₄, 65) (dual of [150, 28, 66]-code), using constructionÂ X with VarÅ¡amov bound based on

linear OA(4¹²¹, 148, F₄, 65) (dual of [148, 27, 66]-code), using
- 2 times truncation [i] based on linear OA(4¹²³, 150, F₄, 67) (dual of [150, 27, 68]-code), using
  - concatenation of two codes [i] based on
    1. linear OA(64¹⁶, 25, F₆₄, 16) (dual of [25, 9, 17]-code or 25-arc in PG(15,64)), using
      - discarding factors / shortening the dual code based on linear OA(64¹⁶, 64, F₆₄, 16) (dual of [64, 48, 17]-code or 64-arc in PG(15,64)), using
        Reedâ€“Solomon code RS(48,64) [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]
linear OA(4¹²¹, 149, F₄, 64) (dual of [149, 28, 65]-code), using Gilbertâ€“VarÅ¡amov bound and b^mÂ = 4¹²¹Â > V_b^sâˆ’1(kâˆ’1)Â = 6 912020 144722 562290 704626 711890 942348 414284 798536 014467 859565 116304 822944 [i]
linear OA(4⁰, 1, F₄, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
  - OA with only one run / dual of code without redundancy [i]

Mode: Linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OA(4¹²³, 152, F₄, 65) (dual of [152, 29, 66]-code)	[i]		ConstructionÂ X with VarÅ¡amov Bound