# American Institute of Mathematical Sciences

November  2018, 12(4): 629-639. doi: 10.3934/amc.2018037

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

 1 Department of Mathematics, University of Delhi, Delhi-110 007, India 2 Mata Sundri College for Women (University of Delhi), Mata Sundri Lane, Delhi-110 002, India

* Corresponding author: Namita Sharma

Received  April 2015 Revised  March 2017 Published  September 2018

Fund Project: The first author is supported by a R & D grant of University of Delhi 2014-15. The second author is supported by Junior Research Fellowship Grant AA/139/F-177 of University Grants Commission.

Alves, Panek and Firer (Error-block codes and poset metrics, Adv. Math. Commun., 2 (2008), 95-111) classified all poset block structures which turn the [8,4,4] extended binary Hamming code into a 1-perfect poset block code. However, the proof needs corrections that are supplied in this paper. We provide a counterexample to show that the extended binary Golay code is not 1-perfect for the proposed poset block structures. All poset block structures turning the extended binary and ternary Golay codes into 1-perfect codes are classified.

Citation: B. K. Dass, Namita Sharma, Rashmi Verma. Characterization of extended Hamming and Golay codes as perfect codes in poset block spaces. Advances in Mathematics of Communications, 2018, 12 (4) : 629-639. doi: 10.3934/amc.2018037
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