The geometry of Hermitian self-orthogonal codes

We prove that if $$n >k^2$$ n > k 2 then a k-dimensional linear code of length n over $${\mathbb F}_{q^2}$$ F q 2 has a truncation which is linearly equivalent to a Hermitian self-orthogonal linear code. In the contrary case we prove that truncations of linear codes to codes equivalent to Hermitian self-orthogonal linear codes occur when the columns of a generator matrix of the code do not impose independent conditions on the space of Hermitian forms. In the case that there are more than n common zeros to the set of Hermitian forms which are zero on the columns of a generator matrix of the code, the additional zeros give the extension of the code to a code that has a truncation which is equivalent to a Hermitian self-orthogonal code.

Entropy-based image encryption using Orthogonal Variable Spreading Factor (OVSF)

The purpose of image encryption is to provide data privacy and security. The former ensures that only authorized personnel can access the original content, while the latter implies that there is no evident relationship between the encrypted and the original content, and that the key space is equally likely and large enough. In the current state of the field, there are several proposals of image encryption techniques with very high privacy (in terms of entropy) but weak in terms of security (i.e., small key space). Recently, a new encoding-based method that provides a long key space (namely 8,57 × 10506) with a middle value of entropy (87%) was proposed. Our proposal preserves the strength of the image encryption methods based on encoding, but with a higher value placed on security than the preliminary works. Every pixel of an image is mapped into an orthogonal code based on 256 bits. The 8-OVSF codes are selected to encode the image, given that the entropy of the inter-symbol is near the possible maximum. Numerous test results verify that our ciphered data have a very high value of entropy (98,5%) with an equally likely and long key space (8,57 × 10506), thus providing an adequate balance between privacy and security.