Dual codes of projective planes of order 25

@article{Clark2003DualCO,
  title={Dual codes of projective planes of order 25},
  author={K. L. Clark and Leslie D. Hatfield and Jennifer D. Key and Harold N. Ward},
  journal={Advances in Geometry},
  year={2003},
  volume={3},
  pages={140-152}
}
We determine improved bounds for the minimum weight of the dual code over F5 of any projective plane of order 25 and describe configurations that could give words of mini- mum weight. 

A lower bound for the minimum weight of the dual 7-ary code of a projective plane of order 49

TLDR
Combinatorial arguments are used to improve the range of bounds on the minimum weight d⊥ of the dual 7-ary code of a projective plane of order 49, noting that the upper bound can be taken to be 91 if the plane has a Baer subplane, as in the desarguesian case.

The Dual Code of Points and t-Spaces in the Projective Space

TLDR
The most important results on C1/t (n; q), the dual code of points and t-spaces in PG(n, q) are presented and a recent result about the classi cation of the small weight codewords in C 1/n-1( n, q), q even, is given.

The minimum weight of dual codes from projective planes

TLDR
This talk will provide a survey of what is known of the p-ary codes from projective planes of order divisible by p, what progress has been made recently, and give some new bounds for planes of some specific orders.

Embedded antipodal planes and the minimum weight of the dual code of points and lines in projective planes of order $p^2$

The minimum weight of the code generated by the incidence matrix of points versus lines in a projective plane has been known for over 50 years. Surprisingly, finding the minimum weight of the dual

Contemporary Mathematics Linear codes from projective spaces

The linear code Cs,t(n, q) of s-spaces and t-spaces in a projective space PG(n, q), q = ph, p prime, is defined as the vector space spanned over Fp by the rows of the incidence matrix of s-spaces and

Linear codes from projective spaces

TLDR
This paper gives an overview of what is currently known about the codes C-s,C-t(n,q) and their duals.

References

SHOWING 1-10 OF 19 REFERENCES

Dual Codes of Translation Planes

We improve on the known upper bound for the minimum weight of the dual codes of translation planes of certain orders by providing a general construction of words of small weight. We use this

Geometric Codes over Fields of Odd Prime Power Order

We obtain improved bounds for the minimum weight of the dual codes associated with the codes from finite geometries in the case of odd order, and some results that apply also to the dual codes of

On the spectrum of the valuesk for which a completek- cap in PG(n, q) exists

Abstractthe aim of this paper is to collect all results on the spectrum of values k that occur as the cardinality of a complete k- cap in a finite projective space. 1

Small sets of even type and codewords

We examine some geometric configurations of points in designs that give rise to vectors in the codes associated with the designs. In particular we look at small sets of points in projective planes of

Designs and their codes

TLDR
The standard geometric codes are presented, followed by a list of recommended designs and some examples of how these designs might be implemented in the real world.

The Translation Planes of Order Twenty-Five

Block designs

The Fp span of the incidence matrix of a finite projective plane

This paper investigates the F span of the rows of an incidence matrix of a finite projective plane. Results are obtained on the dimension and minimum weight (in the sense of algebraic coding theory)

Classical arcs in PG(r, q) for 23 leq q leq 29