Jon-Lark Kim

Learn More
Low-density parity-check (LDPC) codes are serious contenders to turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m/spl ges/2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m,q) on 2q/sup m/ vertices, which(More)
It is well known that the problem of finding stabilizer quantum-error-correcting codes (QECC) is transformed into the problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to classify the extremal additive circulant self-dual codes of lengths up to 15, and construct good codes for lengths(More)
LDPC codes are serious contenders to Turbo codes in terms of decoding performance. One of the main problems is to give an explicit construction of such codes whose Tanner graphs have known girth. For a prime power q and m ≥ 2, Lazebnik and Ustimenko construct a q-regular bipartite graph D(m, q) on 2qm vertices, which has girth at least 2dm/2e+ 4. We regard(More)
In this paper, new binary extremal self-dual codes are presented. A number of new extremal singly-even self-dual codes of lengths 48; 64 and 78, and extremal doubly-even self-dual codes of lengths 80 and 88, are constructed. We also relate an extremal doubly-even self-dual code of length divisible by 24 to an extremal singly-even self-dual code of that(More)
We give a generalized CSS construction for nonbinary quantum error-correcting codes. Using this we construct nonbinary quantum stabilizer codes from algebraic curves. We also give asymptotically good nonbinary quantum codes from a GarciaStichtenoth tower of function fields which are constructible in polynomial time. keywords Algebraic geometric codes,(More)
Abstract—In this paper we classify all extremal and s-extremal binary self-dual codes of length 38. There are exactly 2744 extremal [38, 19, 8] self-dual codes, two s-extremal [38, 19, 6] codes, and 1730 s-extremal [38, 19, 8] codes. We obtain our results from the use of a recursive algorithm used in the recent classification of all extremal self-dual codes(More)
We construct new MDS or near-MDS self-dual codes over large finite fields. In particular, we show that there exists a Euclidean self-dual MDS code of length n = q over GF(q) whenever q = 2<sup>m</sup> (m ges 2) using a Reed-Solomon (RS) code and its extension. It turns out that this multiple description source (MDS) self-dual code is an extended duadic(More)
Linear Complementary Dual codes (LCD) are binary linear codes that meet their dual trivially. We construct LCD codes using orthogonal matrices, self-dual codes, combinatorial designs and Gray map from codes over the family of rings Rk. We give a linear programming bound on the largest size of an LCD code of given length and minimum distance. We make a table(More)