On the construction of completely regular linear codes from distance — Regular graphs

1989 ◽  
pp. 376-393
Author(s):  
Josep Rifà I Coma
Keyword(s):  
Linear Codes ◽  
Regular Graphs ◽  
Completely Regular ◽  
Distance Regular Graphs

scholarly journals Families of nested completely regular codes and distance-regular graphs

2015 ◽  
Vol 9 (2) ◽  
pp. 233-246 ◽  
Author(s):  
Joaquim Borges ◽  
◽  
Josep Rifà ◽  
Victor A. Zinoviev ◽  
◽  
...  
Keyword(s):  
Regular Graphs ◽  
Completely Regular ◽  
Distance Regular Graphs ◽  
Regular Codes ◽  
Completely Regular Codes

scholarly journals Some Families of Orthogonal Polynomials of a Discrete Variable and their Applications to Graphs and Codes

10.37236/172 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
M. Cámara ◽  
J. Fàbrega ◽  
M. A. Fiol ◽  
E. Garriga
Keyword(s):  
Orthogonal Polynomials ◽  
Regular Graphs ◽  
Discrete Variable ◽  
Completely Regular ◽  
Local Distance ◽  
Distance Regular Graphs ◽  
Regular Codes ◽  
Completely Regular Codes ◽  
Orthogonal Systems ◽  
Spectral Characterizations

We present some related families of orthogonal polynomials of a discrete variable and survey some of their applications in the study of (distance-regular) graphs and (completely regular) codes. One of the main peculiarities of such orthogonal systems is their non-standard normalization condition, requiring that the square norm of each polynomial must equal its value at a given point of the mesh. For instance, when they are defined from the spectrum of a graph, one of these families is the system of the predistance polynomials which, in the case of distance-regular graphs, turns out to be the sequence of distance polynomials. The applications range from (quasi-spectral) characterizations of distance-regular graphs, walk-regular graphs, local distance-regularity and completely regular codes, to some results on representation theory.

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