Rigidity Theorems for Partial Linear Spaces

Inamdar, S.P.

doi:10.1006/jcta.2001.3203

Cited by 2 publications

(4 citation statements)

References 6 publications

(3 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where C is the p-ary code of an arbitrary incidence system (Theorem 2). This theorem is a generalisation of the main theorem of [7] which studied the case of partial linear spaces.…”

Section: Introductionmentioning

confidence: 91%

See 1 more Smart Citation

Projective Geometric Codes

Bagchi

Inamdar

2002

Journal of Combinatorial Theory, Series A

Self Cite

View full text Add to dashboard Cite

In this article, we determine the words of minimum weight in the code of the incidence system of s-versus t-flats in a finite projective space. Our proof depends on a few combinatorial results on the geometry of flats which may be of independent interest. We also give bounds for the minimum weight of the dual of this code and show that they are attained in many cases. The lower bound is a consequence of a general result on the dual code of an incidence system. # 2002 Elsevier Science (USA)

show abstract

“…where C is the p-ary code of an arbitrary incidence system (Theorem 2). This theorem is a generalisation of the main theorem of [7] which studied the case of partial linear spaces.…”

Section: Introductionmentioning

confidence: 91%

“…Let D ¼ ðX ; B; IÞ be an incidence system and Y be a subset of X : By the incidence system induced on Y by D we mean the incidence system ðY ; B; I \ ðY Â BÞÞ: We now have the following generalisation of the main theorem of [7] (which is the case l ¼ 1).…”

Section: General Incidence Systemsmentioning

confidence: 96%

Projective Geometric Codes

Bagchi

Inamdar

2002

Journal of Combinatorial Theory, Series A

Self Cite

View full text Add to dashboard Cite

show abstract

“…2 + 1, and the minimum weight words of C p (π) are the non-zero scalar multiples of lines. Also, Inamdar [10] proved that, in this case, the minimum weight words of C ⊥ p (π) are precisely the non-zero scalar multiples of the pairwise differences of lines of π.…”

Section: Coding Theorymentioning

confidence: 98%

“…Using this theorem, one can write an alternative proof of Theorem 4.5. However, since D has ten lines, this alternative proof works only for p > 2 10 . We have chosen to work with P since it has fewer lines.…”

Section: Speculationsmentioning

confidence: 99%

A coding theoretic approach to the uniqueness conjecture for projective planes of prime order

Bagchi

2019

Des. Codes Cryptogr.

View full text Add to dashboard Cite

An outstanding folklore conjecture asserts that, for any prime p, up to isomorphism the projective plane P G(2, F p ) over the field F p := Z/pZ is the unique projective plane of order p. Let π be any projective plane of order p. For any partial linear space X , define the inclusion number i(X , π) to be the number of isomorphic copies of X in π. In this paper we prove that if X has at most log 2 p lines, then i(X , π) can be written as an explicit rational linear combination (depending only on X and p) of the coefficients of the complete weight enumerator (c.w.e.) of the p-ary code of π. Thus, the c.w.e. of this code carries an enormous amount of structural information about π. In consequence, it is shown that if p > 2 9 = 512, and π has the same c.w.e. as P G(2, F p ), then π must be isomorphic to P G(2, F p ). Thus, the uniqueness conjecture can be approached via a thorough study of the possible c.w.e. of the codes of putative projective planes of prime order.

show abstract

Rigidity Theorems for Partial Linear Spaces

Cited by 2 publications

References 6 publications

Projective Geometric Codes

Projective Geometric Codes

A coding theoretic approach to the uniqueness conjecture for projective planes of prime order

Contact Info

Product

Resources

About