MinT - Information on Result #1011880

Information on Result #1011880

Linear OOA(4¹²⁴, 2796253, F₄, 3, 13) (dual of [(2796253, 3), 8388635, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(4¹⁵, 52, F₄, 3, 6) (dual of [(52, 3), 141, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4⁵, 41, F₄, 3, 3) (dual of [(41, 3), 118, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(4⁵, 41, F₄, 2, 3) (dual of [(41, 2), 77, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(4⁵, 41, F₄, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
        a cap found by Tallinii [i]
  2. linear OOA(4¹⁰, 26, F₄, 3, 6) (dual of [(26, 3), 68, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (4, 10, 26)-net over F₄, using
      - linear code embedding found in a computer search [i]
linear OOA(4¹⁰⁹, 2796201, F₄, 3, 13) (dual of [(2796201, 3), 8388494, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4¹⁰⁹, large, F₄, 13) (dual of [large, large−109, 14]-code), using
  - the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [0,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(4¹²⁴, 1398126, F₄, 15, 13) (dual of [(1398126, 15), 20971766, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row