Geodesic
Natural metrics and their properties. P.~1. Submetrics and overmetrics
Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 49-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

Criteria for integer-valued function $\mu\colon X\times X\to\{0,1,\dots\}$ to be a metric (where $X$ is a finite set) are given. Notions of submetric, overmetric, natural and canonical metrics are introduced. Classification of metrics admitting no more than 5 values is constructed, some of their submetrics and overmetrics are described. 
@article{MVK_2011_2_a3,
     author = {B. A. Pogorelov and M. A. Pudovkina},
     title = {Natural metrics and their properties. {P.~1.} {Submetrics} and overmetrics},
     journal = {Matemati\v{c}eskie voprosy kriptografii},
     pages = {49--74},
     publisher = {mathdoc},
     volume = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MVK_2011_2_a3/}
}
TY  - JOUR
AU  - B. A. Pogorelov
AU  - M. A. Pudovkina
TI  - Natural metrics and their properties. P.~1. Submetrics and overmetrics
JO  - Matematičeskie voprosy kriptografii
PY  - 2011
SP  - 49
EP  - 74
VL  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MVK_2011_2_a3/
LA  - ru
ID  - MVK_2011_2_a3
ER  - 
%0 Journal Article
%A B. A. Pogorelov
%A M. A. Pudovkina
%T Natural metrics and their properties. P.~1. Submetrics and overmetrics
%J Matematičeskie voprosy kriptografii
%D 2011
%P 49-74
%V 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MVK_2011_2_a3/
%G ru
%F MVK_2011_2_a3
B. A. Pogorelov; M. A. Pudovkina. Natural metrics and their properties. P.~1. Submetrics and overmetrics. Matematičeskie voprosy kriptografii, Tome 2 (2011), pp. 49-74. http://geodesic.mathdoc.fr/item/MVK_2011_2_a3/

[1] Gabidulin E. M., “Teoriya kodov s maksimalnym rangovym rasstoyaniem”, Problemy peredachi informatsii, 21:1 (1985), 3–16 | MR | Zbl

[2] Kshevetskii A. S., Razrabotka novykh kodov v rangovoi metrike i kriptosistem s otkrytym klyuchom, Diss. kand. fiz.-mat. nauk, MFTI, 2007

[3] Levenshtein V. I., “O sovershennykh kodakh v metrike vypadenii i vstavok”, Diskretnaya matematika, 3:1 (1991), 3–20 | MR | Zbl

[4] Muzychuk M. E., “Podskhemy skhemy Khemminga”, Issledov. po algebr. teorii kombin. ob'ektov, Trudy seminara, VNIISI, M., 1985, 49–76 | MR

[5] Pogorelov B. A., “Podmetriki metriki Khemminga i teorema A. A. Markova”, Trudy po diskretnoi matematike, 9, Fizmatlit, M., 2006, 190–219

[6] Pogorelov B. A., Pudovkina M. A., “Podmetriki metriki Khemminga i preobrazovaniya, rasprostranyayuschie iskazheniya v zadannoe chislo raz”, Trudy po diskretnoi matematike, 10, Fizmatlit, M., 2007, 202–238

[7] Pogorelov B. A., Pudovkina M. A., “Podmetriki Khemminga i ikh gruppy izometrii”, Trudy po diskretnoi matematike, 11, no. 2, Fizmatlit, M., 2008, 147–191

[8] Sidelnikov V. M., “Assotsiativnye skhemy i metriki na konechnoi gruppe”, Dokl. RAN, 396:4 (2004), 455–459 | MR

[9] Sidelnikov V. M., “Assotsiativnye skhemy i avtomorfizmy konechnykh grupp”, Mater. VIII Mezhdunar. sem. “Diskretnaya matematika i ee prilozheniya”, izd-vo MGU, M., 2004, 19–26

[10] Deza M. M., Deza E., Encyclopedia of Distances, Springer-Verlag, 2009, 590 pp. | MR