Let X be an algebraic curve of genus g > 2 defined over a field Fq of characteristic p > 0. From X , under certain conditions, we can construct an algebraic geometry code C. If the code C is self-orthogonal under the symplectic product then we can construct a quantum code Q, called a QAG-code. In this paper we study the construction of such codes from curves with automorphisms and the relation ...

1 Morse code polynomials Morse code sequences are finite sequences of dots (•) and dashes (−). If a dot has length 1 and a dash has length 2 then the number of all such sequences of total length n−1 is the Fibonacci number Fn, which is defined as the sequence of numbers satisfying the recursion Fn = Fn−1 + Fn−2 with initial conditions F0 = 0 and F1 = 1. If a dash is assumed to have length j, j≥...

The evolution of the genetic code has been speculated by many authors, but all of them lack determinative proofs. Jukes [4] inferred the evolution from mitochondrial codes, which are different from the universal codes in some respects. He postulated an archetypal code containing 14 amino acids, from which the universal code could evolve by gene duplication followed by mutational changes. This p...

This paper describes an in-code approach to automatic algebraic-based software testing and a number of useful design patterns for doing it. The approach uses algebras as testable views on a system. These views form test interfaces which are highly automatable. Specifications are expressed in terms of axioms of the algebras. We use the testing tool T2 to provide automation. T2 works with in-code...

In this paper, a method to design regular (2, dc)LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping ...

In this paper, a method to design regular (2, dc)-LDPC codes over GF(q) with both good waterfall and error floor properties is presented, based on the algebraic properties of their binary image. First, the algebraic properties of rows of the parity check matrix H associated with a code are characterized and optimized to improve the waterfall. Then the algebraic properties of cycles and stopping...

The stabilizer code is the most general algebraic construction of quantum error-correcting codes proposed so far. A stabilizer code can be constructed from a self-orthogonal subspace of a symplectic space over a finite field. We propose a construction method of such a selforthogonal space using an algebraic curve. By using the proposed method we construct an asymptotically good sequence of bina...

Minimum storage regenerating codes have minimum storage of data in each node and therefore are maximal distance separable (MDS for short) codes. Thus, the number of nodes is upper bounded by 2, where b is the bits of data stored in each node. From both theoretical and practical points of view (see the details in Section 1), it is natural to consider regenerating codes that nearly have minimum s...

We prove that every algebraic curve X/Q is birational over C to a Teichmüller curve. keywords: algebraic curve, mapping class group, Teichmüller curve, Veech group. MSC code: 32G15, 37D40.