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Linear Codes and Self-Polarity

This page contains a study of projective self-dual (PSD) and self-polar linear codes over finite fields with q elements, where q is a power of a prime. The possible parameters for which PSD codes may exist are presented, and many examples of such codes are given. Algorithms for checking whether a q-ary linear code is self-polar are described. Numerous PSD and self-polar codes over fields with 2, 3, 4, and 5 elements, having two and three nonzero weights, are constructed.

Detailed description can be found here.


There is a separate directory for every type of the studied codes, named according to the number of weights (2W or 3W) and the characteristic of the fi eld - binary, ternary, quaternary and GF5. Files, containing the generator matrices of all constructed codes, are named n_k_d.q_m.


Projective self-dual and self-polar binary two-weight codes - Results can be found here

Projective self-dual and self-polar ternary two-weight codes - Results can be found here

Projective self-dual and self-polar quaternary two-weight codes - Results can be found here

Projective self-dual and self-polar two-weight codes over GF(5) - Results can be found here


Projective self-dual and self-polar binary three-weight codes - Results can be found here

Projective self-dual and self-polar ternary three-weight codes - Results can be found here

Projective self-dual and self-polar quaternary three-weight codes - Results can be found here


Strongly regular graphs corresponding to PTW codes - Results can be found here

References associated with the obtained results


  I. Bouyukliev, S. Bouyuklieva, M. Dzhumalieva-Stoeva and D. Bikov, Linear Codes and Self-Polarity, preprint.