Perfect codes in poset spaces and poset block spaces

Finite Fields and Their Applications ◽

10.1016/j.ffa.2017.02.003 ◽

2017 ◽

Vol 46 ◽

pp. 90-106 ◽

Cited By ~ 4

Author(s):

B.K. Dass ◽

Namita Sharma ◽

Rashmi Verma

Keyword(s):

Perfect Codes ◽

Block Spaces

Download Full-text

Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces

Advances in Mathematics of Communications ◽

10.3934/amc.2018037 ◽

2018 ◽

Vol 12 (4) ◽

pp. 629-639

Author(s):

B. K. Dass ◽

◽

Namita Sharma ◽

Rashmi Verma ◽

Keyword(s):

Perfect Codes ◽

Block Spaces ◽

Golay Codes

Download Full-text

Perfect codes in poset block spaces

Asian-European Journal of Mathematics ◽

10.1142/s179355711750005x ◽

2017 ◽

Vol 10 (01) ◽

pp. 1750005

Author(s):

B. K. Dass ◽

Namita Sharma ◽

Rashmi Verma

Keyword(s):

Block Structure ◽

Block Code ◽

Sufficient Condition ◽

Necessary And Sufficient Condition ◽

Perfect Codes ◽

Minimal Elements ◽

Block Spaces ◽

Hamming Metric ◽

Limited Class ◽

Necessary And Sufficient

There is a limited class of perfect codes with respect to the classical Hamming metric. There are other kind of metrics with respect to which perfect codes have been investigated viz. poset metric, block metric and poset block metric. Given the minimal elements of a poset, a necessary and sufficient condition for [Formula: see text]-perfectness of a poset block code has been derived. A necessary and sufficient condition for a poset block code to be [Formula: see text]-perfect has also been considered. Further, for each [Formula: see text], [Formula: see text], a sufficient condition that ensures the existence of a poset block structure which turns a given code into an [Formula: see text]-perfect poset block code has been obtained. Several illustrations of well known codes to be [Formula: see text]-perfect for specific values of [Formula: see text] have been explored.

Download Full-text