Error-correcting codes in attenuated space over finite fields

Several bounds on the size of ( n + l , M , d , ( m , 0 ) ) q codes in attenuated space over finite fields are provided in this paper. Then, we prove that codes in attenuated space attain the Wang-Xing-Safavi-Naini bound if and only if they are certain Steiner structures.

[1]  Moshe Schwartz,et al.  Codes and Anticodes in the Grassman Graph , 2002, J. Comb. Theory, Ser. A.

[2]  Alexander Vardy,et al.  Error-Correcting Codes in Projective Space , 2011, IEEE Trans. Inf. Theory.

[3]  Shu-Tao Xia,et al.  Johnson type bounds on constant dimension codes , 2007, Des. Codes Cryptogr..

[4]  Reihaneh Safavi-Naini,et al.  Linear authentication codes: bounds and constructions , 2001, IEEE Trans. Inf. Theory.

[5]  Frank R. Kschischang,et al.  Coding for Errors and Erasures in Random Network Coding , 2008, IEEE Trans. Inf. Theory.

[6]  Kaishun Wang,et al.  Singular linear space and its applications , 2011, Finite Fields Their Appl..

[7]  Rudolf Ahlswede,et al.  On Perfect Codes and Related Concepts , 2001, Des. Codes Cryptogr..

[8]  Kaishun Wang,et al.  Association schemes based on attenuated spaces , 2010, Eur. J. Comb..

[9]  F. MacWilliams,et al.  The Theory of Error-Correcting Codes , 1977 .