By using totally isotropic subspaces in an orthogonal space Ä+(2i, 2), several infinite families of packings of 2k -dimensional subspaces of real 2i -dimensional space are constructed, some of which are shown to be optimal packings. A certain Clifford group underlies the construction and links this problem with Barnes-Wall lattices, Kerdock sets and quantum-error-correcting codes.

New single asymmetric error-correcting codes are proposed. These codes are better than existing codes when the code length n is greater than 10, except for n = 12 and n = 15. In many cases one can construct a code C containing at least d2=ne codewords. It is known that a code with jCj d2=(n + 1)e can be easily obtained. It should be noted that the proposed codes for n = 12 and n = 15 are also t...

As the number of learners of English is constantly growing, automatic error correction of ESL learners’ writing is an increasingly active area of research. However, most research has mainly focused on errors concerning articles and prepositions even though tense/aspect errors are also important. One of the main reasons why tense/aspect error correction is difficult is that the choice of tense/a...

Several methods for classifying self-orthogonal codes up to equivalence are presented. These methods are used to classify self-orthogonal codes with largest possible minimum distance over the fields F3 and F4 for lengths n ≤ 29 and small dimensions (up to 6). Some properties of the classified codes are also presented. In particular, an extensive collection of quantum error-correcting codes is o...

In this correspondence, we study binary asymmetric errorcorrecting codes. A general construction for binary asymmetric error-correcting codes is presented. We show that some previously known lower bounds for binary asymmetric error-correcting codes can be obtained from this general construction. Furthermore, some new lower bounds for binary asymmetric error-correcting codes are obtained from th...

The joint source channel coding problem of transmitting a pair of correlated sources over a 2−user MAC is considered. A new concatenated coding scheme, comprising of an inner code of fixed block-length and an outer code of arbitrarily large block-length, is proposed. Its information theoretic performance is analyzed to derive a new set of sufficient conditions. An example is identified to demon...

We give a new construction of nonlinear error-correcting codes over suitable finite fields k from the geometry of modular curves with many rational points over k, combining two recent improvements on Goppa’s construction. The resulting codes are asymptotically the best currently known.

It is known that one can do quantum error correction without syndrome measurement, which is often done in operator quantum error correction (OQEC). However, the physical realization could be challenging, especially when the recovery process involves high-rank projection operators and a superoperator. We use operator theory to improve OQEC so that the implementation can always be done by unitary...

The theory of error-correcting codes is a vast and fast-moving area with many open problems. The objective of this paper is to survey where the current boundaries of knowledge are in a few selected areas, by listing the smallest unsolved cases. Our hope is that these lists will motivate further computational to move these boundaries.