caa a22 4500 47580760X CHVBK 20180406123751.0 cr unu---uuuuu 170329e20001001xx s 000 0 eng 10.1023/A:1008356131869 doi (NATIONALLICENCE)springer-10.1023/A:1008356131869 New Linear Codes Over $$\mathbb{F}_3 $$ and $$\mathbb{F}_5 $$and Improvements on Bounds [Elektronische Daten] [Irfan Siap, Dijen Ray-Chaudhuri] One of the most important problems of coding theory is to constructcodes with best possible minimum distances. In this paper, we generalize the method introduced by [8] and obtain new codes which improve the best known minimum distance bounds of some linear codes. We have found a new linear ternary code and 8 new linear codes over $$\mathbb{F}_5 $$ with improved minimumdistances. First we introduce a generalized version of Gray map,then we give definition of quasi cyclic codes and introduce nearlyquasi cyclic codes. Next, we give the parameters of new codeswith their generator matrices. Finally, we have included twotables which give Hamming weight enumerators of these new codes. Kluwer Academic Publishers, 2000 Quasi cyclic codes nationallicence nearly quasi cyclic codes nationallicence new codes nationallicence improved bounds nationallicence Siap Irfan Department of Mathematics, The Ohio State University, USA aut Ray-Chaudhuri Dijen Department of Mathematics, The Ohio State University, USA aut Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 223-233 0925-1022 21:1-3<223 2000 21 10623 https://doi.org/10.1023/A:1008356131869 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1008356131869 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Siap Irfan Department of Mathematics, The Ohio State University, USA aut NATIONALLICENCE 700 1- Ray-Chaudhuri Dijen Department of Mathematics, The Ohio State University, USA aut NATIONALLICENCE 773 0- Designs, Codes and Cryptography Kluwer Academic Publishers 21/1-3(2000-10-01), 223-233 0925-1022 21:1-3<223 2000 21 10623 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer