Abstract: Systems or apparatus, methods, data structures and/or computer programs are provided for implementing an OLAP system that has increased query execution speed, requires reduced data storage capacity for an OLAP system and/or facilitates scaling of an OLAP system to large data cubes. The OLAP system can advantageously be implemented as an all-main memory OLAP system.

Abstract: Generating a check matrix includes defining a generator function operable to yield check bits associated with a word. A set of primitive elements is calculated from the generator function. A set of check matrix columns is generated, where each check matrix column includes a matrix having a subset of the set of primitive elements. A check matrix is generated from a subset of the set of check matrix columns, where the check matrix yields a syndrome that comprises an error pattern for the word. The check matrix is reported.

Abstract: Generating a check matrix includes defining a set of column vectors. A matrix operable to have a plurality of entries is initiated. Each entry has a submatrix that includes a function of a subset of the set of column vectors. The following is repeated until a last entry of the matrix is reached. Subsets of the set of column vectors are generated from the set of column vectors, and an entry is generated from each subset. A weight associated with each entry is calculated, and an entry having a minimum weight is selected. The selected entry is added to the matrix, and the subset of column vectors associated with the selected entry is removed from the set of column vectors. The matrix is reported.

Abstract: Transmitting data includes receiving a serial sequence of code words. Each code word includes a word and check bits, where the word includes a sequence of word symbols, and the check bits includes a sequence of check bit symbols. The following is repeated until a last word symbol of a last code word is reached: selecting a next code word, and inserting a next word symbol of the selected code word into a vector. The following is repeated until a last check bit symbol of the last code word is reached: selecting a next code word, and inserting a next check bit symbol of the selected code word into the vector. The vector is transmitted.

Abstract: Generating a check matrix includes defining a generator function operable to yield check bits associated with a word. A set of primitive elements is calculated from the generator function. A set of check matrix columns is generated, where each check matrix column includes a matrix having a subset of the set of primitive elements. A check matrix is generated from a subset of the set of check matrix columns, where the check matrix yields a syndrome that comprises an error pattern for the word. The check matrix is reported.