# Bounds for unrestricted codes, by linear programming

@inproceedings{Delsarte1972BoundsFU, title={Bounds for unrestricted codes, by linear programming}, author={Philippe Delsarte}, year={1972} }

The paper describes a problem of linear programming associated with distance properties of unrestricted codes. As a solution to the problem, one obtains an .upper bound for the number of words in codes having a prescribed set of distances. 1. Introduetion Important information about a code is contained in its Hamming distance distribution, defined as follows: for a q-ary code C of length n, it is the (n + 1)tuple (Ao(C), A1(C), ... , AII(C)), where A1(C) denotes the mean number of codewords…

## 163 Citations

УДК 53 B. Mounits NEW UPPER BOUNDS FOR NONBINARY CODES

- Mathematics
- 2012

New upper bounds on codes are presented. The bounds are obtained by linear and semidefinite programming. INTRODUCTION One of the central problems in coding theory is to find upper bounds on maximum…

Bilinear Forms over a Finite Field, with Applications to Coding Theory

- MathematicsJ. Comb. Theory, Ser. A
- 1978

Distance Enumerators for Number-Theoretic Codes

- Computer Science2021 IEEE International Symposium on Information Theory (ISIT)
- 2021

This paper presents an identity of the distance enumerators for the number-theoretic codes and derives the Hamming distance enumerator for the Varshamov-Tenengolts (VT) codes.

A table of upper bounds for binary codes

- Computer ScienceIEEE Trans. Inf. Theory
- 2001

Using previous upper bounds on the size of constant-weight binary codes, known methods are reapply to generate a table of bounds on A(n, d) for all n/spl les/28, which extends the range of parameters compared with previously known tables.

An improvement of the Johnson bound for subspace codes

- Computer ScienceArXiv
- 2017

Improved upper bounds based on the Johnson bound and a connection to divisible codes are given and a characterization of the lengths of full-length $q^r$-divisible $\mathbb{F}_q$-linear codes is presented in a purely geometrical way.

Quantum error detection II: Bounds

- Computer ScienceIEEE Trans. Inf. Theory
- 2000

This part shows that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent and formulates two linear programming problems that are convenient for the analysis of specific short codes.

Energy bounds for codes in polynomial metric spaces

- Mathematics, Computer ScienceAnalysis and Mathematical Physics
- 2019

A unified treatment for obtaining bounds on the potential energy of codes in the general context of polynomial metric spaces (PM-spaces) and the common features of the Levenshtein’s universal upper bounds for the cardinality of codes with given separation are emphasized.

Linear Programming Bounds on the Kissing Number of q-ary Codes

- Computer Science2021 IEEE Information Theory Workshop (ITW)
- 2021

Besides the classical estimation of the probability of decoding error and of undetected error, this work outlines recent applications in hardware protection against side-channel attacks using code-based masking countermeasures, where the protection is all the more efficient a s the kissing number is low.

A Note on the Stability Number of an Orthogonality Graph

- MathematicsEur. J. Comb.
- 2007

A note on the stability number of an orthogonality graph

- Mathematics
- 2007

We consider the orthogonality graph Ω(n) with 2n vertices corresponding to the vectors {0, 1}n , two vertices adjacent if and only if the Hamming distance between them is n/2. We show that, for n =…

## References

SHOWING 1-3 OF 3 REFERENCES

Algebraic coding theory

- Computer ScienceMcGraw-Hill series in systems science
- 1968

This is the revised edition of Berlekamp's famous book, "Algebraic Coding Theory," originally published in 1968, wherein he introduced several algorithms which have subsequently dominated engineering…

The theory of groups, MacmiIlan

- IEEE Trans. Information Theory IT-I7,
- 1964

Orthogonal polynomials, American Mathematical Society Colloquium Publications

- Vol. XXIII,
- 1959